Group Colorings and DP-Colorings of Multigraphs Using Edge-Disjoint Decompositions
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DOI: 10.1007/s00373-021-02345-2
Abstract: In (J Graph Theory 4:241–242, 1980), Burr proved that $$\chi (G)\le m_1m_2 \ldots m_k$$ if and only if G is the edge-disjoint union of k graphs $$G_1,G_2,\ldots ,G_k$$ such that $$\chi (G_i)\le m_i$$ for $$1\le… read more here.
Keywords: number; chromatic number; group; edge disjoint ... See more keywords
The Power of Cut-Based Parameters for Computing Edge-Disjoint Paths
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DOI: 10.1007/s00453-020-00772-w
Abstract: This paper revisits the classical edge-disjoint paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths… read more here.
Keywords: disjoint paths; edge disjoint; edge; cut ... See more keywords
The Vertex-Disjoint and Edge-Disjoint Ramsey Numbers of a Set of Graphs
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DOI: 10.3390/axioms14070486
Abstract: The Ramsey number R(F) of a graph F without isolated vertices is the smallest positive integer n such that every red–blue coloring of Kn produces a subgraph isomorphic to F all of whose edges are colored the same. Let F be… read more here.
Keywords: edge disjoint; vertex disjoint; disjoint ramsey; ramsey ... See more keywords