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### Strong edge colorings of graphs

Odile Favaron, Hao Li, R.H. Schelp
1996 Discrete Mathematics
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.  ...

### Strong edge colorings of uniform graphs

Andrzej Czygrinow, Brendan Nagle
2004 Discrete Mathematics
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.  ...

### Strong edge-coloring of planar graphs

Dávid Hudák, Borut Lužar, Roman Soták, Riste Škrekovski
2014 Discrete Mathematics
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).  ...

### Adjacent strong edge coloring of graphs

Zhongfu Zhang, Linzhong Liu, Jianfang Wang
2002 Applied Mathematics Letters
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.  ...

### Strong edge-coloring of planar graphs

Lian-Ying Miao, Wen-Yao Song
2017 Discussiones Mathematicae Graph Theory
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.  ...

### r-Strong edge colorings of graphs

S. Akbari, H. Bidkhori, N. Nosrati
2006 Discrete Mathematics
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).  ...

### List strong edge coloring of some classes of graphs [article]

Watcharintorn Ruksasakchai, Tao Wang
2017 arXiv   pre-print
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.  ...

### Strong Edge-Coloring of Cubic Bipartite Graphs: A Counterexample [article]

Daniel W. Cranston
2021 arXiv   pre-print
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.  ...

### Strong edge-coloring of (3, Δ)-bipartite graphs [article]

Julien Bensmail
2015 arXiv   pre-print
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.  ...

### Strong edge coloring of Cayley graphs and some product graphs [article]

Suresh Dara, Suchismita Mishra, Narayanan Narayanan, Zsolt Tuza
2021 arXiv   pre-print
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.  ...

### Strong edge coloring of subcubic bipartite graphs [article]

Borut Lužar and Martina Mockovčiaková and Roman Soták and Riste Škrekovski
2013 arXiv   pre-print
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  ...

### Strong List Edge Coloring of Subcubic Graphs

Hongping Ma, Zhengke Miao, Hong Zhu, Jianhua Zhang, Rong Luo
2013 Mathematical Problems in Engineering
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).  ...

### Strong Edge Coloring of Generalized Petersen Graphs

Ming Chen, Lianying Miao, Shan Zhou
2020 Mathematics
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  . A significant amount of interesting papers were devoted to strong edge coloring of graphs.  ...

### Incidence and strong edge colorings of graphs

Richard A. Brualdi, Jennifer J. Quinn Massey
1993 Discrete Mathematics
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  ...

### A Strong Edge-Coloring of Graphs with Maximum Degree 4 Using 22 Colors [article]

Daniel Cranston
2006 arXiv   pre-print
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.  ...
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