Coloring, List Coloring, and Painting Squares of Graphs (and other related problems)
DW Cranston - arXiv preprint arXiv:2210.05915, 2022 - arxiv.org
arXiv:2210.05915v2 [math.CO] 22 Apr 2023 Page 1 arXiv:2210.05915v2 [math.CO] 22 Apr
2023 Coloring, List Coloring, and Painting Squares of Graphs (and other related problems) …
2023 Coloring, List Coloring, and Painting Squares of Graphs (and other related problems) …
Strong chromatic index of graphs with maximum degree four
M Huang, M Santana, G Yu - arXiv preprint arXiv:1806.07012, 2018 - arxiv.org
A strong edge-coloring of a graph $ G $ is a coloring of the edges such that every color class
induces a matching in $ G $. The strong chromatic index of a graph is the minimum number …
induces a matching in $ G $. The strong chromatic index of a graph is the minimum number …
A stronger bound for the strong chromatic index
H Bruhn, F Joos - Combinatorics, Probability and Computing, 2018 - cambridge.org
We prove χ′ s (G)≤ 1.93 Δ (G) 2 for graphs of sufficiently large maximum degree where χ′
s (G) is the strong chromatic index of G. This improves an old bound of Molloy and Reed. As …
s (G) is the strong chromatic index of G. This improves an old bound of Molloy and Reed. As …
A stronger bound for the strong chromatic index
H Bruhn, F Joos - Electronic Notes in Discrete Mathematics, 2015 - Elsevier
We prove χ s′(G)≤ 1.93 Δ (G) 2 for graphs of sufficiently large maximum degree where χ
s′(G) is the strong chromatic index of G. This improves an old bound of Molloy and Reed …
s′(G) is the strong chromatic index of G. This improves an old bound of Molloy and Reed …
Recent progress on strong edge-coloring of graphs
K Deng, G Yu, X Zhou - Discrete Mathematics, Algorithms and …, 2019 - World Scientific
Recent progress on strong edge-coloring of graphs Page 1 Discrete Mathematics, Algorithms
and Applications Vol. 11, No. 5 (2019) 1950062 (21 pages) c© World Scientific Publishing …
and Applications Vol. 11, No. 5 (2019) 1950062 (21 pages) c© World Scientific Publishing …
Proper conflict-free list-coloring, odd minors, subdivisions, and layered treewidth
CH Liu - Discrete Mathematics, 2024 - Elsevier
Proper conflict-free coloring is an intermediate notion between proper coloring of a graph
and proper coloring of its square. It is a proper coloring such that for every non-isolated …
and proper coloring of its square. It is a proper coloring such that for every non-isolated …
[HTML][HTML] Lower bounds on the complexity of MSO1 model-checking
Kreutzer and Tazari proved in 2010 that MSO 2 model-checking is not polynomial (XP) wrt
the formula size as parameter for graph classes that are subgraph-closed and whose tree …
the formula size as parameter for graph classes that are subgraph-closed and whose tree …
[HTML][HTML] On strong edge-colouring of subcubic graphs
A strong edge-colouring of a graph G is a proper edge-colouring such that every path of
length 3 uses three different colours. In this paper we improve some previous results on the …
length 3 uses three different colours. In this paper we improve some previous results on the …
[HTML][HTML] The strong chromatic index of a class of graphs
J Wu, W Lin - Discrete mathematics, 2008 - Elsevier
The strong chromatic index of a graph G is the minimum integer k such that the edge set of G
can be partitioned into k induced matchings. Faudree et al.[RJ Faudree, RH Schelp, A …
can be partitioned into k induced matchings. Faudree et al.[RJ Faudree, RH Schelp, A …