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Upper Bounds for the Strong Chromatic Index of Halin Graphs
Discussiones Mathematicae Graph Theory, 2018 The strong chromatic index of a graph G, denoted by χ′s(G), is the minimum number of vertex induced matchings needed to partition the edge set of G. Let T be a tree without vertices of degree 2 and have at least one vertex of degree greater than 2.
Hu Ziyu, Lih Ko-Wei, Liu Daphne Der-Fen
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Color code techniques in rainbow connection
Electronic Journal of Graph Theory and Applications, 2018 Let G be a graph with an edge k-coloring γ : E(G) → {1, …, k} (not necessarily proper). A path is called a rainbow path if all of its edges have different colors.
Fendy Septyanto, Kiki A. Sugeng
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Strong edge colorings of uniform graphs
Discrete Mathematics, 2004 A strong edge coloring of a graph is a (proper) edge coloring in which every color class is an induced matching. The strong chromatic index \(\chi_S(G)\) of a graph \(G\) is the minimum number of colors in a strong edge coloring of \(G\). For a bipartite graph \(G=(U\cup V, E)\), and for two nonempty sets \(U'\subseteq U\) and \(V'\subseteq V\), let ...
Czygrinow, Andrzej, Nagle, Brendan
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Strong edge-coloring of cubic bipartite graphs: A counterexample
Discrete Applied Mathematics, 2022 A strong edge-coloring $φ$ of a graph $G$ assigns colors to edges of $G$ such that $φ(e_1)\ne φ(e_2)$ whenever $e_1$ and $e_2$ are at distance no more than 1. It is equivalent to a proper vertex coloring of the square of the line graph of $G$. In 1990 Faudree, Schelp, Gyárfás, and Tuza conjectured that if $G$ is a bipartite graph with maximum degree 3 ...
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Adjacent strong edge coloring of graphs
Applied Mathematics Letters, 2002 A proper edge coloring of a graph is an adjacent strong edge coloring if, for every adjacent vertices \(u\) and \(v\), the set of colors of all edges at \(u\) is different from the set of all colors of edges at \(v\). The authors determine the minimum number \(k\) such that a tree (a cycle, a complete graph) has an adjacent strong edge coloring with ...
Zhang, Zhongfu +2 more
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Placement Delivery Arrays from Combinations of Strong Edge Colorings [PDF]
2019 Ninth International Workshop on Signal Design and its Applications in Communications (IWSDA), 2019 It has recently been pointed out in both of the works [C. Shanguan, Y. Zhang, and G. Ge, {\em IEEE Trans. Inform. Theory}, 64(8):5755-5766 (2018)] and [Q. Yan, X. Tang, Q. Chen, and M. Cheng, {\em IEEE Commun. Lett.}, 22(2):236-239 (2018)] that placement delivery arrays (PDAs), as coined in [Q. Yan, M. Cheng, X. Tang, and Q.
Jerod Michel, Qi Wang
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Optimal strong parity edge-coloring of complete graphs [PDF]
Combinatorica, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bunde, David P. +3 more
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FEBS Letters, EarlyView.This perspective highlights emerging insights into how the circadian transcription factor CLOCK:BMAL1 regulates chromatin architecture, cooperates with other transcription factors, and coordinates enhancer dynamics. We propose an updated framework for how circadian transcription factors operate within dynamic and multifactorial chromatin landscapes ...
Xinyu Y. Nie, Jerome S. Menet
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Strong edge-colorings for $$k$$ k -degenerate graphs
Graphs and Combinatorics, 2014 We prove that the strong chromatic index for each $k$-degenerate graph with maximum degree $ $ is at most $(4k-2) -k(2k-1)+1$.
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Multiple ETS family transcription factors bind mutant p53 via distinct interaction regions
FEBS Letters, EarlyView.Mutant p53 gain‐of‐function is thought to be mediated by interaction with other transcription factors. We identify multiple ETS transcription factors that can bind mutant p53 and found that this interaction can be promoted by a PXXPP motif. ETS proteins that strongly bound mutant p53 were upregulated in ovarian cancer compared to ETS proteins that ...
Stephanie A. Metcalf +6 more
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