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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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Edge-group choosability of outerplanar and near-outerplanar graphs [PDF]
Transactions on Combinatorics, 2020 Let $\chi_{gl}(G)$ be the {\it{group choice number}} of $G$. A graph $G$ is called {\it{edge-$k$-group choosable}} if its line graph is $k$-group choosable. The {\it{group-choice index}} of $G$, $\chi'_{gl}(G)$, is the smallest $k$ such that $G$ is edge-$
Amir Khamseh
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A note on recognizing an old friend in a new place:list coloring and the zero-temperature Potts model [PDF]
, 2014 Here we observe that list coloring in graph theory coincides with the zero-temperature antiferromagnetic Potts model with an external field. We give a list coloring polynomial that equals the partition function in this case. This is analogous to the well-
A. Ellis-Monaghan, Joanna, Moffatt, Iain
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Between coloring and list-coloring: μ-coloring
Electronic Notes in Discrete Mathematics, 2005 A new variation of the coloring problem, μ-coloring, is defined in this paper. A coloring of a graph G = (V,E) is a function f : V → N such that f(v) 6= f(w) if v is adjacent to w. Given a graph G = (V,E) and a function μ : V → N, G is μ-colorable if it admits a coloring f with f(v) ≤ μ(v) for each v ∈ V .
Bonomo, Flavia +1 more
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Planar Graphs with the Distance of 6--Cycles at Least 2 from Each Other Are DP-3-Colorable
Mathematics, 2020 DP-coloring as a generalization of list coloring was introduced by Dvořák and Postle recently. In this paper, we prove that every planar graph in which the distance between 6−-cycles is at least 2 is DP-3-colorable, which extends the result of Yin and Yu
Yueying Zhao, Lianying Miao
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Discussiones Mathematicae Graph Theory, 2013 Given a graph G = (V,E) and a set Lv of admissible colors for each vertex v ∈ V (termed the list at v), a list coloring of G is a (proper) vertex coloring ϕ : V → S v2V Lv such that ϕ(v) ∈ Lv for all v ∈ V and ϕ(u) 6= ϕ(v) for all uv ∈ E.
Tuza Zsolt
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An Analogue of DP-Coloring for Variable Degeneracy and its Applications
Discussiones Mathematicae Graph Theory, 2022 A graph G is list vertex k-arborable if for every k-assignment L, one can choose f(v) ∈ L(v) for each vertex v so that vertices with the same color induce a forest. In [6], Borodin and Ivanova proved that every planar graph without 4-cycles adjacent to 3-
Sittitrai Pongpat, Nakprasit Kittikorn
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Discrete Mathematics, 2000 Let \(R= \{1,2,\dots, r\}\) be a set of colors, and let \(\ell: V(G)\to 2^R\) be a function. A proper coloring \(c: V(G)\to R\) is said to be a list coloring if \(c(x)\in\ell(x)\) for all \(x\). If there is an integer \(s\) such that all functions \(\ell\) with \(|\ell(x)|= s\) have a list coloring, then \(G\) is said to be \(s\)-choosable. The authors
Albertson, Michael O. +2 more
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Additive List Coloring of Planar Graphs with Given Girth
Discussiones Mathematicae Graph Theory, 2020 An additive coloring of a graph G is a labeling of the vertices of G from {1, 2, . . . , k} such that two adjacent vertices have distinct sums of labels on their neighbors.
Brandt Axel +2 more
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Toward an Axiomatization of Strongly Possible Functional Dependencies
Vietnam Journal of Computer Science, 2021 In general, there are two main approaches to handle the missing data values problem in SQL tables. One is to ignore or remove any record with some missing data values.
Munqath Alattar, Attila Sali
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