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Discussiones Mathematicae Graph Theory, 2023 DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute +3 more
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b-Coloring of the Mycielskian of Some Classes of Graphs
Discussiones Mathematicae Graph Theory, 2022 The b-chromatic number b(G) of a graph G is the maximum k for which G has a proper vertex coloring using k colors such that each color class contains at least one vertex adjacent to a vertex of every other color class.
Raj S. Francis, Gokulnath M.
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Gallai-Ramsey Numbers for Rainbow S3+S_3^ + and Monochromatic Paths
Discussiones Mathematicae Graph Theory, 2022 Motivated by Ramsey theory and other rainbow-coloring-related problems, we consider edge-colorings of complete graphs without rainbow copy of some fixed subgraphs.
Li Xihe, Wang Ligong
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A Note on Edge-Group Choosability of Planar Graphs without 5-Cycles
Journal of Mathematics, 2020 This paper is devoted to a study of the concept of edge-group choosability of graphs. We say that G is edge-k-group choosable if its line graph is k-group choosable.
Amir Khamseh
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Linear List Coloring of Some Sparse Graphs
Discussiones Mathematicae Graph Theory, 2021 A linear k-coloring of a graph is a proper k-coloring of the graph such that any subgraph induced by the vertices of any pair of color classes is a union of vertex-disjoint paths. A graph G is linearly L-colorable if there is a linear coloring c of G for
Chen Ming, Li Yusheng, Zhang Li
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A weak form of Hadwiger's conjecture [PDF]
, 2013 We introduce the following weak version of Hadwiger's conjecture: If $G$ is a graph and $\kappa$ is a cardinal such that there is no coloring map $c:G \to \kappa$, then $K_\kappa$ is a minor of $G$.
van der Zypen, Dominic
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DICHROMATIC NUMBER AND FRACTIONAL CHROMATIC NUMBER
Forum of Mathematics, Sigma, 2016 The dichromatic number of a graph $G$ is the maximum integer $k$
BOJAN MOHAR, HEHUI WU
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Conflict-Free Vertex Connection Number At Most 3 and Size of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in a vertex-coloured graph is called conflict-free if there is a colour used on exactly one of its vertices. A vertex-coloured graph is said to be conflict-free vertex-connected if any two distinct vertices of the graph are connected by a conflict-
Doan Trung Duy, Schiermeyer Ingo
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Surface Embeddability of Graphs via Joint Trees [PDF]
, 2011 This paper provides a way to observe embedings of a graph on surfaces based on join trees and then characterizations of orientable and nonorientable embeddabilities of a graph with given ...
Liu, Yanpei
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An Improved Upper Bound on Neighbor Expanded Sum Distinguishing Index
Discussiones Mathematicae Graph Theory, 2020 A total k-weighting f of a graph G is an assignment of integers from the set {1, . . . , k} to the vertices and edges of G. We say that f is neighbor expanded sum distinguishing, or NESD for short, if Σw∈N(v) (f(vw) + f(w)) differs from Σw∈N(u)(f(uw) + f(
Vučković Bojan
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