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Strong edge colorings of graphs
1996
Discrete Mathematics
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Suppose that G has no 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. ...
doi:10.1016/0012-365x(95)00102-3
fatcat:4pp5xumttbfctaaenxd5katf7i
Strong edge colorings of uniform graphs
2004
Discrete Mathematics
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for a related class 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. ...
doi:10.1016/j.disc.2004.04.011
fatcat:elfddcxpyjhudio6kfr46uoure
Strong edge-coloring of planar graphs
2014
Discrete Mathematics
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2013 pre-print arXiv:1303.4580v1 fatcat:253uveramzao7a6jzrdc6uydsqOther Versions
A 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). ...
doi:10.1016/j.disc.2014.02.002
fatcat:alll7hnllraatc6txk6s2dt4gy
Adjacent strong edge coloring of graphs
2002
Applied Mathematics Letters
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For a 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. ...
doi:10.1016/s0893-9659(02)80015-5
fatcat:ftbab72zsnbgpegffukvbpa674
Strong edge-coloring of planar graphs
2017
Discussiones Mathematicae Graph Theory
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A 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. ...
doi:10.7151/dmgt.1951
fatcat:523gddnjyverdktiwegzxpybbu
r-Strong edge colorings of graphs
2006
Discrete Mathematics
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Wang, Adjacent 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). ...
doi:10.1016/j.disc.2004.12.027
fatcat:wokoo75sqnb3vhu2twiy5cgz5a
List strong edge coloring of some classes of graphs
[article]
2017
arXiv
pre-print
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A 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. ...
arXiv:1402.5677v3
fatcat:ez2tcbqf7zdjthbbcrpqlhqewy
Strong Edge-Coloring of Cubic Bipartite Graphs: A Counterexample
[article]
2021
arXiv
pre-print
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A 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. ...
arXiv:2112.01443v3
fatcat:er7v2j4qhve6hp7tji6jvw6opi
Strong edge-coloring of (3, Δ)-bipartite graphs
[article]
2015
arXiv
pre-print
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A 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. ...
arXiv:1412.2624v2
fatcat:jbj6yny4zzboha5k4lp5uiftly
Strong edge coloring of Cayley graphs and some product graphs
[article]
2021
arXiv
pre-print
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A 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. ...
arXiv:2107.00718v2
fatcat:kucjgzdiprgtbc7qh2ls52skge
Strong edge coloring of subcubic bipartite graphs
[article]
2013
arXiv
pre-print
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A 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 ...
arXiv:1311.6668v2
fatcat:af5boh3gdbhzpowkw7btt3ummi
Strong List Edge Coloring of Subcubic Graphs
2013
Mathematical Problems in Engineering
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We study 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). ...
doi:10.1155/2013/316501
fatcat:kn4ksfswfjhcznni5usx5rhgxa
Strong Edge Coloring of Generalized Petersen Graphs
2020
Mathematics
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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. ...
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. ...
doi:10.3390/math8081265
fatcat:w7zqbvdxnnbzxd4bcf3jyymd3m
Incidence and strong edge colorings of graphs
1993
Discrete Mathematics
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The incidence 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 ...
doi:10.1016/0012-365x(93)90286-3
fatcat:heezguw2rnf5nmqvrzwvwr77wm
A Strong Edge-Coloring of Graphs with Maximum Degree 4 Using 22 Colors
[article]
2006
arXiv
pre-print
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In 1985, Erdős and Neśetril conjectured that the 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. ...
arXiv:math/0601623v1
fatcat:m26e5jsz4betfgr7z6ca6dctza
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