The Experts below are selected from a list of 7320 Experts worldwide ranked by ideXlab platform
Sergey Pupyrev - One of the best experts on this subject based on the ideXlab platform.
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threshold coloring and Unit Cube contact representation of planar graphs
Discrete Applied Mathematics, 2017Co-Authors: Md Jawaherul Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey Pupyrev, Jackson ToeniskoetterAbstract:Abstract In this paper we study threshold-coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. A pair of vertices with a small difference in their colors implies that the edge between them is present, while a pair of vertices with a big color difference implies that the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. Variants of the threshold-coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another.
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threshold coloring and Unit Cube contact representation of graphs
Workshop on Graph-Theoretic Concepts in Computer Science, 2013Co-Authors: Jawaherul Md Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey PupyrevAbstract:We study threshold coloring of graphs where the vertex colors, represented by integers, describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. We show the NP-completeness for two variants of the threshold coloring problem and describe a polynomial-time algorithm for another.
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threshold coloring and Unit Cube contact representation of graphs
arXiv: Discrete Mathematics, 2013Co-Authors: Md Jawaherul Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey PupyrevAbstract:In this paper we study threshold coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs without short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. Variants of the threshold coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another.
Jawaherul Md Alam - One of the best experts on this subject based on the ideXlab platform.
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threshold coloring and Unit Cube contact representation of graphs
Workshop on Graph-Theoretic Concepts in Computer Science, 2013Co-Authors: Jawaherul Md Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey PupyrevAbstract:We study threshold coloring of graphs where the vertex colors, represented by integers, describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. We show the NP-completeness for two variants of the threshold coloring problem and describe a polynomial-time algorithm for another.
Michael Kaufmann - One of the best experts on this subject based on the ideXlab platform.
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threshold coloring and Unit Cube contact representation of planar graphs
Discrete Applied Mathematics, 2017Co-Authors: Md Jawaherul Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey Pupyrev, Jackson ToeniskoetterAbstract:Abstract In this paper we study threshold-coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. A pair of vertices with a small difference in their colors implies that the edge between them is present, while a pair of vertices with a big color difference implies that the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. Variants of the threshold-coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another.
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threshold coloring and Unit Cube contact representation of graphs
Workshop on Graph-Theoretic Concepts in Computer Science, 2013Co-Authors: Jawaherul Md Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey PupyrevAbstract:We study threshold coloring of graphs where the vertex colors, represented by integers, describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. We show the NP-completeness for two variants of the threshold coloring problem and describe a polynomial-time algorithm for another.
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threshold coloring and Unit Cube contact representation of graphs
arXiv: Discrete Mathematics, 2013Co-Authors: Md Jawaherul Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey PupyrevAbstract:In this paper we study threshold coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs without short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. Variants of the threshold coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another.
Stephen G Kobourov - One of the best experts on this subject based on the ideXlab platform.
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threshold coloring and Unit Cube contact representation of planar graphs
Discrete Applied Mathematics, 2017Co-Authors: Md Jawaherul Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey Pupyrev, Jackson ToeniskoetterAbstract:Abstract In this paper we study threshold-coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. A pair of vertices with a small difference in their colors implies that the edge between them is present, while a pair of vertices with a big color difference implies that the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. Variants of the threshold-coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another.
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threshold coloring and Unit Cube contact representation of graphs
Workshop on Graph-Theoretic Concepts in Computer Science, 2013Co-Authors: Jawaherul Md Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey PupyrevAbstract:We study threshold coloring of graphs where the vertex colors, represented by integers, describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. We show the NP-completeness for two variants of the threshold coloring problem and describe a polynomial-time algorithm for another.
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threshold coloring and Unit Cube contact representation of graphs
arXiv: Discrete Mathematics, 2013Co-Authors: Md Jawaherul Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey PupyrevAbstract:In this paper we study threshold coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs without short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. Variants of the threshold coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another.
Steven Chaplick - One of the best experts on this subject based on the ideXlab platform.
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threshold coloring and Unit Cube contact representation of planar graphs
Discrete Applied Mathematics, 2017Co-Authors: Md Jawaherul Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey Pupyrev, Jackson ToeniskoetterAbstract:Abstract In this paper we study threshold-coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. A pair of vertices with a small difference in their colors implies that the edge between them is present, while a pair of vertices with a big color difference implies that the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. Variants of the threshold-coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another.
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threshold coloring and Unit Cube contact representation of graphs
Workshop on Graph-Theoretic Concepts in Computer Science, 2013Co-Authors: Jawaherul Md Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey PupyrevAbstract:We study threshold coloring of graphs where the vertex colors, represented by integers, describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. We show the NP-completeness for two variants of the threshold coloring problem and describe a polynomial-time algorithm for another.
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threshold coloring and Unit Cube contact representation of graphs
arXiv: Discrete Mathematics, 2013Co-Authors: Md Jawaherul Alam, Steven Chaplick, Gasper Fijavž, Michael Kaufmann, Stephen G Kobourov, Sergey PupyrevAbstract:In this paper we study threshold coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs without short cycles can always be threshold-colored. Using these results we obtain Unit-Cube contact representation of several subclasses of planar graphs. Variants of the threshold coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another.
