scholarly journals On the strong chromatic index and maximum induced matching of tree-cographs, permutation graphs and chordal bipartite graphs

2015 ◽  
Vol 30 ◽  
pp. 21-28 ◽  
Author(s):  
Ton Kloks ◽  
Sheung-Hung Poon ◽  
Chin-Ting Ung ◽  
Yue-Li Wang
Keyword(s):  
Bipartite Graphs ◽  
Chromatic Index ◽  
Permutation Graphs ◽  
Induced Matching ◽  
Strong Chromatic Index ◽  
Maximum Induced Matching ◽  
Chordal Bipartite Graphs

scholarly journals The strong chromatic index of (3,Δ)-bipartite graphs

2017 ◽  
Vol 340 (5) ◽  
pp. 1143-1149 ◽  
Author(s):  
Mingfang Huang ◽  
Gexin Yu ◽  
Xiangqian Zhou
Keyword(s):  
Bipartite Graphs ◽  
Chromatic Index ◽  
Strong Chromatic Index

scholarly journals On the induced matching problem in hamiltonian bipartite graphs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yinglei Song
Keyword(s):  
Bipartite Graph ◽  
Parameterized Complexity ◽  
Bipartite Graphs ◽  
Matching Problem ◽  
Induced Matching ◽  
Subexponential Time ◽  
Maximum Induced Matching

Abstract In this paper, we study the parameterized complexity of the induced matching problem in hamiltonian bipartite graphs and the inapproximability of the maximum induced matching problem in hamiltonian bipartite graphs. We show that, given a hamiltonian bipartite graph, the induced matching problem is W[1]-hard and cannot be solved in time n o ⁢ ( k ) {n^{o(\sqrt{k})}} , where n is the number of vertices in the graph, unless the 3SAT problem can be solved in subexponential time. In addition, we show that unless NP = P {\operatorname{NP}=\operatorname{P}} , a maximum induced matching in a hamiltonian bipartite graph cannot be approximated within a ratio of n 1 / 4 - ϵ {n^{1/4-\epsilon}} , where n is the number of vertices in the graph.

scholarly journals Strong chromatic index of products of graphs

2007 ◽  
Vol Vol. 9 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Olivier Togni
Keyword(s):  
Cartesian Product ◽  
Complete Graphs ◽  
Chromatic Index ◽  
Induced Matching ◽  
Colour Class ◽  
Strong Chromatic Index ◽  
Minimum Number ◽  
International Audience

Graphs and Algorithms International audience 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. In this paper, we present bounds for strong chromatic index of three different products of graphs in term of the strong chromatic index of each factor. For the cartesian product of paths, cycles or complete graphs, we derive sharper results. In particular, strong chromatic indices of d-dimensional grids and of some toroidal grids are given along with approximate results on the strong chromatic index of generalized hypercubes.

scholarly journals Strong Edge Coloring of Generalized Petersen Graphs

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1265
Author(s):  
Ming Chen ◽  
Lianying Miao ◽  
Shan Zhou
Keyword(s):  
Edge Coloring ◽  
Petersen Graph ◽  
Chromatic Index ◽  
Induced Matching ◽  
Generalized Petersen Graph ◽  
Generalized Petersen Graphs ◽  
Strong Chromatic Index ◽  
Color Class ◽  
Proper Edge Coloring ◽  
Petersen Graphs

A strong edge coloring of a graph G is a proper edge coloring such that every color class is an induced matching. In 2018, Yang and Wu proposed a conjecture that every generalized Petersen graph P(n,k) with k≥4 and n>2k can be strong edge colored with (at most) seven colors. Although the generalized Petersen graph P(n,k) is a kind of special graph, the strong chromatic index of P(n,k) is still unknown. In this paper, we support the conjecture by showing that the strong chromatic index of every generalized Petersen graph P(n,k) with k≥4 and n>2k is at most 9.

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