Results 11 to 20 of about 4,890 (237)
Strong Chromatic Index of Outerplanar Graphs [PDF]
Axioms, 2022 The strong chromatic index χs′(G) of a graph G is the minimum number of colors needed in a proper edge-coloring so that every color class induces a matching in G. It was proved In 2013, that every outerplanar graph G with Δ≥3 has χs′(G)≤3Δ−3.
Ying Wang +3 more
doaj +5 more sources
Strong chromatic index of products of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 The strong chromatic index of a graph is the minimum number of colours needed to colour the edges in such a way that each colour class is an induced matching.
Olivier Togni
doaj +6 more sources
A stronger bound for the strong chromatic index [PDF]
Electronic Notes in Discrete Mathematics, 2015 We prove χ′s(G) ≤ 1.93 Δ(G)2 for graphs of sufficiently large maximum degree where χ′s(G) is the strong chromatic index of G. This improves an old bound of Molloy and Reed. As a by-product, we present a Talagrand-type inequality where we are allowed to exclude unlikely bad outcomes that would otherwise render the inequality unusable.
Henning Brühn, Felix Joos
exaly +5 more sources
The strong chromatic index of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe chromatic index $\chi'(G)$ of a graph $G$ is the smallest $k$ for which $G$ admits an edge $k$-coloring such that any two adjacent edges have distinct colors.
Yiqiao Wang +3 more
doaj +5 more sources
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
doaj +4 more sources
Strong list-chromatic index of subcubic graphs [PDF]
Discrete Mathematics, 2018 A strong $k$-edge-coloring of a graph G is an edge-coloring with $k$ colors in which every color class is an induced matching. The strong chromatic index of $G$, denoted by $χ'_{s}(G)$, is the minimum $k$ for which $G$ has a strong $k$-edge-coloring.
Guanghui Wang, Donglei Yang, Gexin Yu
exaly +6 more sources
Strong Chromatic Index Of Planar Graphs With Large Girth
Discussiones Mathematicae Graph Theory, 2014 Let Δ ≥ 4 be an integer. In this note, we prove that every planar graph with maximum degree Δ and girth at least 1 Δ+46 is strong (2Δ−1)-edgecolorable, that is best possible (in terms of number of colors) as soon as G contains two adjacent vertices of ...
Jennhwa Chang Gerard +3 more
doaj +5 more sources
Strong chromatic index and Hadwiger number [PDF]
Journal of Graph Theory, 2022 AbstractWe investigate the effect of a fixed forbidden clique minor upon the strong chromatic index, both in multigraphs and in simple graphs. We conjecture for each that any ‐minor‐free multigraph of maximum degree has strong chromatic index at most . We present a construction certifying that if true the conjecture is asymptotically sharp as .
Wouter Cames van Batenburg +3 more
+8 more sources
Bounding the strong chromatic index of dense random graphs
Discrete Mathematics, 2004 For a finite simple graph \(G\), a strong edge colouring of \(G\) is an edge colouring in which every colour class is an induced matching. (Since each class is a matching, the colouring is proper.) The strong chromatic index of \(G\), \(\chi_{s}(G)\), is the smallest number of colours in a strong edge colouring of \(G\).
Andrzej Czygrinow
exaly +4 more sources
Strong Chromatic Index of Graphs With Maximum Degree Four [PDF]
The Electronic Journal of Combinatorics, 2018 A strong edge-coloring of a graph $G$ is a coloring of the edges such that every color class induces a matching in $G$. The strong chromatic index of a graph is the minimum number of colors needed in a strong edge-coloring of the graph. In 1985, Erdős and Nešetřil conjectured that every graph with maximum degree $\Delta$ has a strong edge-coloring ...
Mingfang Huang +2 more
+6 more sources