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Strong edge colorings of graphs

1996
*
Discrete Mathematics
*

Suppose that G has no

doi:10.1016/0012-365x(95)00102-3
fatcat:4pp5xumttbfctaaenxd5katf7i
*strong**edge**coloring*with this number*of**colors*and let F be one*of*the proper*edge**colorings*with rcn7*colors*such that (1) ]FB] is as small as possible, and (2) subject to (1 ... This follows by taking a proper*edge**coloring**of*G by A + 1*colors*and modifying it, replacing each*edge**of*a spanning forest by a new*color*. ...##
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Strong edge colorings of uniform graphs

2004
*
Discrete Mathematics
*

for a related class

doi:10.1016/j.disc.2004.04.011
fatcat:elfddcxpyjhudio6kfr46uoure
*of**graphs*G known as uniform or -regular*graphs*. ... Our main tool in proving this statement is a powerful packing result*of*Pippenger and Spencer (Combin. Theory Ser. A 51(1) (1989) 24). ... Introduction For a finite simple*graph*G = (V (G), E(G)), a*strong**edge**coloring**of*G is an*edge**coloring*in which every*color*class is an induced matching. ...##
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Strong edge-coloring of planar graphs

2014
*
Discrete Mathematics
*

A

doi:10.1016/j.disc.2014.02.002
fatcat:alll7hnllraatc6txk6s2dt4gy
*strong**edge**coloring**of*a*graph*is a proper*edge**coloring*where the*edges*at distance at most two receive distinct*colors*. ... It is known that every planar*graph*with maximum degree D has a*strong**edge**coloring*with at most 4D + 4*colors*. ... The smallest number*of**colors*for which a*strong**edge**coloring**of*a*graph*G exists is called the*strong*chromatic index, χ ′ s (G). ...##
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Adjacent strong edge coloring of graphs

2002
*
Applied Mathematics Letters
*

For a

doi:10.1016/s0893-9659(02)80015-5
fatcat:ftbab72zsnbgpegffukvbpa674
*graph*G(V, E), if a proper k-*edge**coloring*f is satisfied with C(u) # C(V) for UZ) E E(G), where C(u) = {f(~v) 1 UZI E E}, then f is called k-adjacent*strong**edge**coloring**of*G. is abbreviated k-ASEC ... , and xbs(G) = min{k 1 k-ASEC*of*G} is called the adjacent*strong**edge*chromatic number*of*G. ... In this paper, we study the adjacent*strong**edge**coloring**of**graphs*. ...##
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Strong edge-coloring of planar graphs

2017
*
Discussiones Mathematicae Graph Theory
*

A

doi:10.7151/dmgt.1951
fatcat:523gddnjyverdktiwegzxpybbu
*strong**edge*-*coloring**of*a*graph*is a proper*edge*-*coloring*where each*color*class induces a matching. ... It is known that every planar*graph*G has a*strong**edge*-*coloring*with at most 4∆(G) + 4*colors*[R.J. Faudree, A. Gyárfás, R.H. Schelp and Zs. ... Acknowledgements The authors would like to express their thanks to the referee for his valuable corrections and suggestions*of*the manuscript that greatly improve the format and correctness*of*it. ...##
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r-Strong edge colorings of graphs

2006
*
Discrete Mathematics
*

Wang, Adjacent

doi:10.1016/j.disc.2004.12.027
fatcat:wokoo75sqnb3vhu2twiy5cgz5a
*strong**edge**coloring**of**graphs*, Appl. Math. Lett. 15 (2002) 623-626] it has been proved that for any tree T with at least three vertices, s (T , 1) (T ) + 1. ... Let G be a*graph*and for any natural number r, s (G, r) denotes the minimum number*of**colors*required for a proper*edge**coloring**of*G in which no two vertices with distance at most r are incident to*edges*... The r-*strong**edge**coloring*number s (G, r) is the minimum number*of**colors*required for an r-*strong**edge**coloring**of*the*graph*G. Clearly for any natural number r, s (G, r) s (G, r + 1). ...##
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List strong edge coloring of some classes of graphs
[article]

2017
*
arXiv
*
pre-print

A

arXiv:1402.5677v3
fatcat:ez2tcbqf7zdjthbbcrpqlhqewy
*strong**edge**coloring**of*a*graph*is a proper*edge**coloring*in which every*color*class is an induced matching. ... The*strong*chromatic index*of*a*graph*is the minimum number*of**colors*needed to obtain a*strong**edge**coloring*. ... This project was supported by the National Natural Science Foundation*of*China (11101125) and partially supported by the Fundamental Research Funds for Universities in Henan. ...##
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Strong Edge-Coloring of Cubic Bipartite Graphs: A Counterexample
[article]

2021
*
arXiv
*
pre-print

A

arXiv:2112.01443v3
fatcat:er7v2j4qhve6hp7tji6jvw6opi
*strong**edge*-*coloring*φ*of*a*graph*G assigns*colors*to*edges**of*G such that φ(e_1)φ(e_2) whenever e_1 and e_2 are at distance no more than 1. ... It is equivalent to a proper vertex*coloring**of*the square*of*the line*graph**of*G. ... Introduction A*strong**edge*-*coloring**strong**edge*-*coloring*ϕ*of*a*graph*G assigns*colors*to the*edges**of*G such that ϕ(e 1 ) = ϕ(e 2 ) whenever e 1 and e 2 are at distance no more than 1. ...##
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Strong edge-coloring of (3, Δ)-bipartite graphs
[article]

2015
*
arXiv
*
pre-print

A

arXiv:1412.2624v2
fatcat:jbj6yny4zzboha5k4lp5uiftly
*strong**edge*-*coloring**of*a*graph*G is an assignment*of**colors*to*edges*such that every*color*class induces a matching. ... For every such*graph*, we prove that a*strong*4Δ-*edge*-*coloring*can always be obtained. ... Greedy*coloring*arguments show that 2∆ 2 − 2∆ + 1 is a naive upper bound on the*strong*chromatic index*of*any*graph*. But so many*colors*are generally not necessary to obtain a*strong**edge*-*coloring*. ...##
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Strong edge coloring of Cayley graphs and some product graphs
[article]

2021
*
arXiv
*
pre-print

A

arXiv:2107.00718v2
fatcat:kucjgzdiprgtbc7qh2ls52skge
*strong**edge**coloring**of*a*graph*G is a proper*edge**coloring**of*G such that every*color*class is an induced matching. The minimum number*of**colors*required is termed the*strong*chromatic index. ... In this paper, we determine the exact value*of*the*strong*chromatic index*of*all unitary Cayley*graphs*. ...*Strong**edge**coloring**of*unitary Cayley*graphs*In this section we determine the*strong*chromatic index*of*all unitary Cayley*graphs*. ...##
###
Strong edge coloring of subcubic bipartite graphs
[article]

2013
*
arXiv
*
pre-print

A

arXiv:1311.6668v2
fatcat:af5boh3gdbhzpowkw7btt3ummi
*strong**edge**coloring**of*a*graph*G is a proper*edge**coloring*in which each*color*class is an induced matching*of*G. ... In 1993, Brualdi and Quinn Massey proposed a conjecture that every bipartite*graph*without 4-cycles and with the maximum degrees*of*the two partite sets 2 and Δ admits a*strong**edge**coloring*with at most ... Introduction A*strong**edge**coloring**of*a*graph*G is a proper*edge**coloring*in which each*color*class is an induced matching*of*G; i.e., any two*edges*at distance at most two are assigned distinct*colors*...##
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Strong List Edge Coloring of Subcubic Graphs

2013
*
Mathematical Problems in Engineering
*

We study

doi:10.1155/2013/316501
fatcat:kn4ksfswfjhcznni5usx5rhgxa
*strong*list*edge**coloring**of*subcubic*graphs*, and we prove that every subcubic*graph*with maximum average degree less than 15/7, 27/11, 13/5, and 36/13 can be strongly list*edge**colored*with six ... , seven, eight, and nine*colors*, respectively. ... Acknowledgments The authors acknowledge the support*of*the National Natural Science Foundation*of*China (nos. 11101351 and 11171288) and NSF*of*University in Jiangsu province (no. 11KJB110014). ...##
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Strong Edge Coloring of Generalized Petersen Graphs

2020
*
Mathematics
*

A

doi:10.3390/math8081265
fatcat:w7zqbvdxnnbzxd4bcf3jyymd3m
*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*. ... The concept*of**strong**edge**coloring*was introduced by Fouquet and Jolivet [1] . A significant amount*of*interesting papers were devoted to*strong**edge**coloring**of**graphs*. ...##
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Incidence and strong edge colorings of graphs

1993
*
Discrete Mathematics
*

The incidence

doi:10.1016/0012-365x(93)90286-3
fatcat:heezguw2rnf5nmqvrzwvwr77wm
*coloring*number turns out to be the*strong*chromatic index*of*an associated bipartite*graph*. ... We define the incidence*coloring*number*of*a*graph*and bound it in terms*of*the maximum degree. ... By the above sq(H') 62A and it is easy to extend a 24*strong**edge**coloring**of*H' to a 24*strong**edge**coloring**of*H. 0 We now prove our conjecture about*strong*chromatic index for bipartite*graphs*whose ...##
###
A Strong Edge-Coloring of Graphs with Maximum Degree 4 Using 22 Colors
[article]

2006
*
arXiv
*
pre-print

In 1985, Erdős and Neśetril conjectured that the

arXiv:math/0601623v1
fatcat:m26e5jsz4betfgr7z6ca6dctza
*strong**edge*-*coloring*number*of*a*graph*is bounded above by 5/4Δ^2 when Δ is even and 1/4(5Δ^2-2Δ+1) when Δ is odd. ... In this paper we give an algorithm that uses at most 22*colors*. ... The exposition*of*this paper has been greatly improved by critique from David Bunde and Erin Chambers. ...
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