Filters








1,672 Hits in 4.5 sec

On the Strong Chromatic Index of Sparse Graphs

Philip DeOrsey, Michael Ferrara, Nathan Graber, Stephen G. Hartke, Luke L. Nelsen, Eric Sullivan, Sogol Jahanbekam, Bernard Lidický, Derrick Stolee, Jennifer White
2018 Electronic Journal of Combinatorics  
The strong chromatic index of a graph $G$, denoted $\chi'_s(G)$, is the least number of colors needed to edge-color $G$ so that edges at distance at most two receive distinct colors.  ...  (G) \geq 41$ then $\chi'_{s,\ell}(G) \leq 5$, answering a question of Borodin and Ivanova [Precise upper bound for the strong edge chromatic number of sparse planar graphs, Discuss.  ...  Acknowledgements This collaboration began as part of the 2014 Rocky Mountain-Great Plains Graduate Research Workshop in Combinatorics.  ... 
doi:10.37236/5390 fatcat:orytssdr3bbxxpuwy6kjtfjofu

On the Strong Chromatic Index of Sparse Graphs [article]

Philip DeOrsey, Jennifer Diemunsch, Michael Ferrara, Nathan Graber, Stephen G. Hartke, Sogol Jahanbekam, Bernard Lidicky, Luke L. Nelsen, Derrick Stolee, Eric Sullivan
2015 arXiv   pre-print
Ivanova [Precise upper bound for the strong edge chromatic number of sparse planar graphs, Discuss.  ...  The strong chromatic index of a graph G, denoted χ_s'(G), is the least number of colors needed to edge-color G so that edges at distance at most two receive distinct colors.  ...  We give sparsity conditions that imply a subcubic planar graph has strong chromatic index at most five and a subquartic planar graph has strong chromatic index at most seven.  ... 
arXiv:1508.03515v1 fatcat:rpyw73c4krgunnw7kzv7vipwsy

Strong edge coloring sparse graphs

Julien Bensmail, Marthe Bonamy, Hervé Hocquard
2015 Electronic Notes in Discrete Mathematics  
A strong edge coloring of a graph is a proper edge coloring such that no edge has two incident edges of the same color.  ...  Erdős and Nešetřil conjectured in 1989 that 5 4 ∆ 2 colors are always enough for a strong edge coloring, where ∆ is the maximum degree of the graph.  ...  For more details on recent improvements on the strong chromatic index of planar graphs, see [2] . Regarding bipartite graphs, the goal is the following conjecture.  ... 
doi:10.1016/j.endm.2015.06.104 fatcat:guxciho55bdutovwerh7qgtzfu

The strong edge colorings of a sparse random graph

Zbigniew Palka
1998 The Australasian Journal of Combinatorics  
In this paper we consider the behavior of the strong chromatic index of a sparse random graph K (n, p), where p = p(n) = 0(1).  ...  The strong chromatic index of a graph G is the smallest integer k such that the edge set E( G) can be partitioned into k induced subgraphs of G which form matchings.  ...  The author is indebted to a referee for constructive suggestions.  ... 
dblp:journals/ajc/Palka98 fatcat:6resg6tsg5exxk4s2s27qmhm24

Algorithms [chapter]

2011 Graph Coloring Problems  
Berge's Conjecture on Edge-Coloring Bibliography 16 Infinite Chromatic Graphs Sparse Subgraphs of High Chromatic Number Infinite Chromatic Subgraphs Almost Bipartite Subgraphs Laree Finite «-Chromatic  ...  200 12.20 List-Edge-Chromatic Numbers 201 12.21 Strong Chromatic Index 202 12.22 Vizing's Interchange Problem 203 12.23 Scheduling Without Waiting Periods 203 Bibliography 205 13 Orientations  ... 
doi:10.1002/9781118032497.ch10 fatcat:374tktuvgvekni4fnz3dgbytjm

Strong chromatic index of k-degenerate graphs

Tao Wang
2014 Discrete Mathematics  
In this note, we improve a result by Dębski [Strong chromatic index of sparse graphs, arXiv:1301.1992v1] and show that the strong chromatic index of a k-degenerate graph G is at most (4k-2) ·Δ(G) - 2k^  ...  The strong chromatic index _s'(G) of a graph G is the minimum number of colors in a strong edge coloring of G.  ...  For more detailed discussion on the strong chromatic index of chordless graphs, we refer the reader to [1] . Remark 3.  ... 
doi:10.1016/j.disc.2014.04.016 fatcat:azi3my7ptnc3jp5wgknuzzfnyu

Strong chromatic index of sparse graphs [article]

Michał Dębski, Jarosław Grytczuk, Małgorzata Śleszyńska-Nowak
2013 arXiv   pre-print
The strong chromatic index of G, denoted by χ_s^'(G), is the least number of colors in a strong edge coloring of G.  ...  A coloring of the edges of a graph G is strong if each color class is an induced matching of G.  ...  The strong chromatic index of G, denoted by χ ′ s (G), is the minimum number of colors in a strong edge coloring of G.  ... 
arXiv:1301.1992v1 fatcat:olsn5rpujjgdfcuh7y327so7yq

The Distance-t Chromatic Index of Graphs

TOMÁŠ KAISER, ROSS J. KANG
2013 Combinatorics, probability & computing  
The other is a bound of O(Δ^t/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.  ...  We obtain two upper bounds for the distance-t chromatic index, the least number of colours necessary for such a colouring.  ...  The complete bipartite graphs K ∆,∆ are regular of arbitrarily large degree ∆, have girth 4 and strong chromatic index ∆ 2 as noted in [4] .  ... 
doi:10.1017/s0963548313000473 fatcat:bvsulk4kmrc4zcwkoutjscgntu

Distance edge-colourings and matchings

Ross J. Kang, Putra Manggala
2012 Discrete Applied Mathematics  
The third is that of an upper bound on the distance chromatic index for sparse random graphs. One of our results gives a counterexample to a conjecture of Skupień.  ...  We consider a distance generalisation of the strong chromatic index and the maximum induced matching number. We study graphs of bounded maximum degree and Erdős-Rényi random graphs.  ...  Acknowledgements The first author is supported by an NWO Veni grant. This research was conducted while he was a postdoctoral fellow at McGill University. He was supported by NSERC (Canada).  ... 
doi:10.1016/j.dam.2012.07.001 fatcat:n72n65lndjbwvoalyj7b3b7xdu

A tribute to Célia P. de Mello

Aurora Morgana, Sheila de Almeida
2022 Matemática contemporânea  
The fruitful and long lasting collaboration of researchers Célia P.  ...  Acknowledgment The authors are grateful to LAWCG 2020 for the opportunity to register such a fruitful and enjoyable cooperation.  ...  The chromatic index of G, χ ′ (G), is the minimum k such that G has a k-edge-coloring. An easy lower bound for the chromatic index of a graph G is the maximum vertex degree ∆(G).  ... 
doi:10.21711/231766362021/rmc4819 fatcat:xltpm6zwsrbznei25dj5mgylxm

Page 1595 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Mah- dian [Random Structures Algorithms 17 (2000), no. 3-4, 357-375; MR 2001k:05076] and determine, up to a constant factor, the strong (list) chromatic index of a random graph.  ...  lists have 5 colours each).” 2003c:05090 = 05C15 05C35 Vu, Van H. (1-UCSD; La Jolla, CA) A general upper bound on the list chromatic number of locally sparse graphs.  ... 

Edge-colouring and total-colouring chordless graphs

Raphael C.S. Machado, Celina M.H. de Figueiredo, Nicolas Trotignon
2013 Discrete Mathematics  
A graph G is chordless if no cycle in G has a chord. In the present work we investigate the chromatic index and total chromatic number of chordless graphs.  ...  We describe a known decomposition result for chordless graphs and use it to establish that every chordless graph of maximum degree Δ≥ 3 has chromatic index Δ and total chromatic number Δ + 1.  ...  The edge-colouring problem or chromatic index problem is the problem of determining the chromatic index of a graph.  ... 
doi:10.1016/j.disc.2013.03.020 fatcat:oye6jvujxzg7zc6pjn7h65gfii

Strong edge-colouring of sparse planar graphs [article]

Julien Bensmail, Hervé Hocquard
2014 arXiv   pre-print
In the last part of the paper, we raise some questions related to a long-standing conjecture of Vizing on proper edge-colouring of planar graphs.  ...  A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching.  ...  An interesting question is to see how the strong chromatic index behaves for sparse planar graphs.  ... 
arXiv:1401.4568v3 fatcat:me52jj5svnbgbpmmg36kg73s2a

Page 6193 of Mathematical Reviews Vol. , Issue 91K [page]

1991 Mathematical Reviews  
The chromatic index problem is known to be NP-complete even for cubic graphs.  ...  This paper addresses the problems of determining the chromatic index of partial k-trees and determining the isomorphism of two such graphs.  ... 

Page 4475 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
In this paper, we consider the behavior of the strong chromatic index of a sparse random graph K (n, p), where p = p(n) =o0(1).” 99:05161 05C85 05C75 68R10 Caro, Yair (IL-HAIF2D; Tivon); Ellingham, M.  ...  Summary: “The strong chromatic index of a graph G is the smallest integer k such that the edge set E(G) can be partitioned into k induced subgraphs of G which form matchings.  ... 
« Previous Showing results 1 — 15 out of 1,672 results