Strong chromatic index of K1,t-free graphs

2020 ◽  
Vol 284 ◽  
pp. 53-60
Author(s):  
Michał Dębski ◽  
Konstanty Junosza-Szaniawski ◽  
Małgorzata Śleszyńska-Nowak
Keyword(s):  
Chromatic Index ◽  
Strong Chromatic Index

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 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.

The strong chromatic index of graphs with edge weight eight

2020 ◽  
Vol 40 (1) ◽  
pp. 227-233
Author(s):  
Lily Chen ◽  
Shumei Chen ◽  
Ren Zhao ◽  
Xiangqian Zhou
Keyword(s):  
Edge Weight ◽  
Chromatic Index ◽  
Strong Chromatic Index

scholarly journals Bounding the strong chromatic index of dense random graphs

2004 ◽  
Vol 281 (1-3) ◽  
pp. 129-136 ◽  
Author(s):  
Andrzej Czygrinow ◽  
Brendan Nagle
Keyword(s):  
Random Graphs ◽  
Chromatic Index ◽  
Strong Chromatic Index

Strong Chromatic Index of 2-Degenerate Graphs

2012 ◽  
Vol 73 (2) ◽  
pp. 119-126 ◽  
Author(s):  
Gerard Jennhwa Chang ◽  
N. Narayanan
Keyword(s):  
Chromatic Index ◽  
Strong Chromatic Index

scholarly journals The Strong Chromatic Index of Random Graphs

2005 ◽  
Vol 19 (3) ◽  
pp. 719-727 ◽  
Author(s):  
Alan Frieze ◽  
Michael Krivelevich ◽  
Benny Sudakov
Keyword(s):  
Random Graphs ◽  
Chromatic Index ◽  
Strong Chromatic Index

scholarly journals The Distance-t Chromatic Index of Graphs

2013 ◽  
Vol 23 (1) ◽  
pp. 90-101 ◽  
Author(s):  
TOMÁŠ KAISER ◽  
ROSS J. KANG
Keyword(s):  
Maximum Degree ◽  
Upper Bounds ◽  
The Other ◽  
Graph Colouring ◽  
Chromatic Index ◽  
Multiplicative Factor ◽  
Strong Chromatic Index ◽  
Absolute Positive Constant ◽  
Large Maximum ◽  
Fixed Positive Integer

We consider two graph colouring problems in which edges at distance at most t are given distinct colours, for some fixed positive integer t. We obtain two upper bounds for the distance-t chromatic index, the least number of colours necessary for such a colouring. One is a bound of (2-ε)Δt for graphs of maximum degree at most Δ, where ε is some absolute positive constant independent of t. The other is a bound of O(Δt/log Δ) (as Δ → ∞) for graphs of maximum degree at most Δ and girth at least 2t+1. The first bound is an analogue of Molloy and Reed's bound on the strong chromatic index. The second bound is tight up to a constant multiplicative factor, as certified by a class of graphs of girth at least g, for every fixed g ≥ 3, of arbitrarily large maximum degree Δ, with distance-t chromatic index at least Ω(Δt/log Δ).

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