3-consecutive edge coloring of a graph

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

Research output: Contribution to journalArticle

2 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 - Feb 6 2012

Fingerprint

Edge Coloring
Coloring
Consecutive
Graph in graph theory
Color
Cut Vertex
Graph Invariants
Graph Classes
Colouring
Efficient Algorithms
Cycle
Path

Keywords

  • 3-consecutive edge coloring
  • Stable cutset
  • Stable k-separator
  • Strongly independent edge coloring

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

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

3-consecutive edge coloring of a graph. / Bujtás, Cs; Sampathkumar, E.; Tuza, Z.; Dominic, Ch; Pushpalatha, L.

In: Discrete Mathematics, Vol. 312, No. 3, 06.02.2012, p. 561-573.

Research output: Contribution to journalArticle

Bujtás, C, Sampathkumar, E, Tuza, Z, Dominic, C & Pushpalatha, L 2012, '3-consecutive edge coloring of a graph', Discrete Mathematics, vol. 312, no. 3, pp. 561-573. https://doi.org/10.1016/j.disc.2011.04.006
Bujtás C, Sampathkumar E, Tuza Z, Dominic C, Pushpalatha L. 3-consecutive edge coloring of a graph. Discrete Mathematics. 2012 Feb 6;312(3):561-573. https://doi.org/10.1016/j.disc.2011.04.006
Bujtás, Cs ; Sampathkumar, E. ; Tuza, Z. ; Dominic, Ch ; Pushpalatha, L. / 3-consecutive edge coloring of a graph. In: Discrete Mathematics. 2012 ; Vol. 312, No. 3. pp. 561-573.
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