3-consecutive edge coloring of a graph

Cs Bujtás, E. Sampathkumar, Zs Tuza, Ch Dominic, L. Pushpalatha

Research output: Article

3 Citations (Scopus)

Abstract

Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or a cycle of length 3. The 3-consecutive edge coloring number ψ′3c(G) of G is the maximum number of colors permitted in a coloring of the edges of G such that if e1, e2 and e3 are consecutive edges in G, then e1 or e3 receives the color of e2. Here we initiate the study of ψ′3c(G). A close relation between 3-consecutive edge colorings and a certain kind of vertex cut is pointed out, and general bounds on ψ′3c are given in terms of other graph invariants. Algorithmically, the distinction between ψ′ 3c=1 and ψ′3c=2 is proved to be intractable, while efficient algorithms are designed for some particular graph classes.

Original languageEnglish
Pages (from-to)561-573
Number of pages13
JournalDiscrete Mathematics
Volume312
Issue number3
DOIs
Publication statusPublished - febr. 6 2012

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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    Bujtás, C., Sampathkumar, E., Tuza, Z., Dominic, C., & Pushpalatha, L. (2012). 3-consecutive edge coloring of a graph. Discrete Mathematics, 312(3), 561-573. https://doi.org/10.1016/j.disc.2011.04.006