A note on M2-edge colorings of graphs | Zendy

Július Czap | Zendy

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A note on M2-edge colorings of graphs

Author(s) -

Július Czap

Publication year - 2014

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2015.35.3.287

Subject(s) - combinatorics , mathematics , edge coloring , vertex (graph theory) , complete coloring , graph , enhanced data rates for gsm evolution , brooks' theorem , discrete mathematics , 1 planar graph , chordal graph , line graph , graph power , computer science , artificial intelligence

An edge coloring \(\varphi\) of a graph \(G\) is called an \(M_2\)-edge coloring if \(|\varphi(v)|\le2 \) for every vertex \(v\) of \(G\), where \(\varphi(v)\) is the set of colors of edges incident with \(v\). Let \(K_2(G)\) denote the maximum numberof colors used in an \(M_2\)-edge coloring of \(G\). Let \(G_1\), \(G_2\) and \(G_3\) be graphs such that \(G_1\subseteq G_2\subseteq G_3\). In this paper we deal with the following question: Assuming that \(K_2(G_1)=K_2(G_3)\), does it hold \(K_2(G_1)=K_2(G_2)=K_2(G_3)\)

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