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On the Strong Chromatic Index of Sparse Graphs

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. ...

##
###
On the Strong Chromatic Index of Sparse Graphs
[article]

2015
*
arXiv
*
pre-print

Ivanova [Precise upper bound for

arXiv:1508.03515v1
fatcat:rpyw73c4krgunnw7kzv7vipwsy
*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. ...##
###
Strong edge coloring sparse graphs

2015
*
Electronic Notes in Discrete Mathematics
*

A

doi:10.1016/j.endm.2015.06.104
fatcat:guxciho55bdutovwerh7qgtzfu
*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. ...##
###
The strong edge colorings of a sparse random graph

1998
*
The Australasian Journal of Combinatorics
*

In this paper we consider

dblp:journals/ajc/Palka98
fatcat:6resg6tsg5exxk4s2s27qmhm24
*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. ...##
###
Algorithms
[chapter]

2011
*
Graph Coloring Problems
*

Berge's Conjecture

doi:10.1002/9781118032497.ch10
fatcat:374tktuvgvekni4fnz3dgbytjm
*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 ...##
###
Strong chromatic index of k-degenerate graphs

2014
*
Discrete Mathematics
*

In this note, we improve a result by Dębski [

doi:10.1016/j.disc.2014.04.016
fatcat:azi3my7ptnc3jp5wgknuzzfnyu
*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. ...##
###
Strong chromatic index of sparse graphs
[article]

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. ...

##
###
The Distance-t Chromatic Index of Graphs

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] . ...

##
###
Distance edge-colourings and matchings

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). ...

##
###
A tribute to Célia P. de Mello

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). ...

##
###
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

2013
*
Discrete Mathematics
*

A

doi:10.1016/j.disc.2013.03.020
fatcat:oye6jvujxzg7zc6pjn7h65gfii
*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*. ...##
###
Strong edge-colouring of sparse planar graphs
[article]

2014
*
arXiv
*
pre-print

In

arXiv:1401.4568v3
fatcat:me52jj5svnbgbpmmg36kg73s2a
*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*. ...##
###
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. ...
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