Results 41 to 50 of about 1,606 (89)
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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Veterinary Dermatology, Volume 36, Issue 6, Page 825-837, December 2025.Background: Inhibition of the Janus kinase pathway is an established treatment for allergic dermatitis. Objective: To evaluate the efficacy and safety of ilunocitinib for control of pruritus in dogs with allergic dermatitis in a randomised, double‐masked clinical trial.
Sophie Forster +5 more
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A unified proof of Brooks' theorem and Catlin's theorem [PDF]
, 2014 We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.Comment: Proof rewritten based on referee's ...
Sivaraman, Vaidy
core
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 Study on Variants of Status Unequal Coloring in Graphs and Its Properties
Journal of Mathematics, Volume 2024, Issue 1, 2024.Let G∧ be a simple connected graph with vertex set ϑG∧ and edge set ξG∧. The status of a vertex p∈ϑG∧ is defined as ∑q≠pd(p, q). A subset P of ϑG∧ is called a status unequal dominating set (stu‐dominating set) of G∧; for every q∈ϑ−P, there exists p in P such that p and q are adjacent and st(p) ≠ st(q).
Parvathy Gnana Sambandam +4 more
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Vertex-Coloring 2-Edge-Weighting of Graphs [PDF]
, 2010 A $k$-{\it edge-weighting} $w$ of a graph $G$ is an assignment of an integer weight, $w(e)\in \{1,\dots, k\}$, to each edge $e$. An edge weighting naturally induces a vertex coloring $c$ by defining $c(u)=\sum_{u\sim e} w(e)$ for every $u \in V(G)$. A $k$
Lu, Hongliang +2 more
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Vertex coloring of plane graphs with nonrepetitive boundary paths
, 2011 A sequence $s_1,s_2,...,s_k,s_1,s_2,...,s_k$ is a repetition. A sequence $S$ is nonrepetitive, if no subsequence of consecutive terms of $S$ form a repetition. Let $G$ be a vertex colored graph.
Alon +12 more
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Generalized Sum List Colorings of Graphs
Discussiones Mathematicae Graph Theory, 2019 A (graph) property 𝒫 is a class of simple finite graphs closed under isomorphisms. In this paper we consider generalizations of sum list colorings of graphs with respect to properties 𝒫.
Kemnitz Arnfried +2 more
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Discussiones Mathematicae Graph Theory, 2020 Metric properties of Hanoi graphs Hnp are not as well understood as those of the closely related, but structurally simpler Sierpiński graphs Snp. The most outstanding open problem is to find the domination number of Hanoi graphs.
Hinz Andreas M., Movarraei Nazanin
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M2-Edge Colorings Of Cacti And Graph Joins
Discussiones Mathematicae Graph Theory, 2016 An edge coloring φ of a graph G is called an M2-edge coloring if |φ(v)| ≤ 2 for every vertex v of G, where φ(v) is the set of colors of edges incident with v. Let 𝒦2(G) denote the maximum number of colors used in an M2-edge coloring of G.
Czap Július +2 more
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