Results 21 to 30 of about 115,444 (312)
The List Edge Coloring and List Total Coloring of Planar Graphs with Maximum Degree at Least 7
Discussiones Mathematicae Graph Theory, 2020 A graph G is edge k-choosable (respectively, total k-choosable) if, whenever we are given a list L(x) of colors with |L(x)| = k for each x ∈ E(G) (x ∈ E(G) ∪ V (G)), we can choose a color from L(x) for each element x such that no two adjacent (or ...
Sun Lin +3 more
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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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A Note on the Equitable Choosability of Complete Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2021 In 2003 Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. A k-assignment, L, for a graph G assigns a list, L(v), of k available colors to each v ∈ V (G), and an equitable L-coloring of G is a ...
Mudrock Jeffrey A. +4 more
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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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Journal of Graph Theory, 2017 AbstractThe dichromatic number of a digraph D is the least number k such that the vertex set of D can be partitioned into k parts each of which induces an acyclic subdigraph. Introduced by Neumann‐Lara in 1982, this digraph invariant shares many properties with the usual chromatic number of graphs and can be seen as the natural analog of the graph ...
Bensmail, Julien +2 more
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AKCE International Journal of Graphs and Combinatorics, 2023 We introduce a concept in graph coloring motivated by the popular Sudoku puzzle. Let [Formula: see text] be a graph of order n with chromatic number [Formula: see text] and let [Formula: see text] Let [Formula: see text] be a k-coloring of the induced ...
J. Maria Jeyaseeli +3 more
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On DP-Coloring of Digraphs [PDF]
, 2018 DP-coloring is a relatively new coloring concept by Dvo\v{r}\'ak and Postle and was introduced as an extension of list-colorings of (undirected) graphs.
Bang-Jensen, Jørgen +3 more
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Criticality, the list color function, and list coloring the cartesian product of graphs [PDF]
Journal of Combinatorics, 2021 We introduce a notion of color-criticality in the context of chromatic-choosability. We define a graph $G$ to be strong $k$-chromatic-choosable if $ (G) = k$ and every $(k-1)$-assignment for which $G$ is not list-colorable has the property that the lists are the same for all vertices.
Kaul, Hemanshu, Mudrock, Jeffrey A.
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The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs
Discussiones Mathematicae Graph Theory, 2017 A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring
Immel Poppy, Wenger Paul S.
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Colorings of Plane Graphs Without Long Monochromatic Facial Paths
Discussiones Mathematicae Graph Theory, 2021 Let G be a plane graph. A facial path of G is a subpath of the boundary walk of a face of G. We prove that each plane graph admits a 3-coloring (a 2-coloring) such that every monochromatic facial path has at most 3 vertices (at most 4 vertices).
Czap Július +2 more
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