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Injective edge coloring of generalized Petersen graphs
AIMS Mathematics, 2021 Three edges $ e_1 $, $ e_2 $ and $ e_3 $ in a graph $ G $ are $ consecutive $ if they form a cycle of length $ 3 $ or a path in this order. A $ k $-$ injective\; edge\; coloring $ of a graph $ G $ is an edge coloring of $ G $, (not necessarily proper ...
Yanyi Li, Lily Chen
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Deterministic Distributed Edge-Coloring via Hypergraph Maximal Matching [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2017 We present a deterministic distributed algorithm that computes a $(2\Delta-1)$-edge-coloring, or even list-edge-coloring, in any $n$-node graph with maximum degree $\Delta$, in $O(\log^7 \Delta \log n)$ rounds.
Fischer, Manuela +2 more
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The Complexity of Distributed Edge Coloring with Small Palettes [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2018 The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1.
Chang, Yi-Jun +4 more
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Strong Edge-Coloring Of Planar Graphs
Discussiones Mathematicae Graph Theory, 2017 A strong edge-coloring of a graph is a proper edge-coloring where each color class induces a matching. We denote by 𝜒's(G) the strong chromatic index of G which is the smallest integer k such that G can be strongly edge-colored with k colors. It is known
Song Wen-Yao, Miao Lian-Ying
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Introduction to dominated edge chromatic number of a graph [PDF]
Opuscula Mathematica, 2021 We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph \(G\), is a proper edge coloring of \(G\) such that each color class is dominated by at least one edge of \(G\).
Mohammad R. Piri, Saeid Alikhani
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Streaming Edge Coloring with Asymptotically Optimal Colors [PDF]
International Colloquium on Automata, Languages and Programming, 2023 Given a graph $G$, an edge-coloring is an assignment of colors to edges of $G$ such that any two edges sharing an endpoint receive different colors. By Vizing's celebrated theorem, any graph of maximum degree $\Delta$ needs at least $\Delta$ and at most $
Soheil Behnezhad, Mohammad Saneian
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Low-Memory Algorithms for Online and W-Streaming Edge Coloring [PDF]
arXiv.org, 2023 For edge coloring, the online and the W-streaming models seem somewhat orthogonal: the former needs edges to be assigned colors immediately after insertion, typically without any space restrictions, while the latter limits memory to sublinear in the ...
Prantar Ghosh, Manuel Stoeckl
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Distributed Edge Coloring in Time Polylogarithmic in Δ [PDF]
ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, 2022 We provide new deterministic algorithms for the edge coloring problem, which is one of the classic and highly studied distributed local symmetry breaking problems. As our main result, we show that a (2Δ - 1)-edge coloring can be computed in time poly log
Alkida Balliu +3 more
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Improved Distributed Algorithms for the Lovász Local Lemma and Edge Coloring [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2022 The Lov\'asz Local Lemma is a classic result in probability theory that is often used to prove the existence of combinatorial objects via the probabilistic method.
Peter Davies
semanticscholar +1 more source
Revisiting semistrong edge‐coloring of graphs [PDF]
Journal of Graph Theory, 2022 A matching M $M$ in a graph G $G$ is semistrong if every edge of M $M$ has an endvertex of degree one in the subgraph induced by the vertices of M $M$ .
Borut Lužar +2 more
semanticscholar +1 more source