Path-bicolorable graphs (Extended Abstract)

Andreas Brandstädt, Martin C. Golumbic, Van Bang Le, Marina Lipshteyn

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this paper, we introduce the notion of path-bicolorability that generalizes bipartite graphs in a natural way: For k ≥ 2, a graph G = (V,E) is P k -bicolorable if its vertex set V can be partitioned into two subsets (i.e., colors) V 1 and V 2 such that for every induced P k (i.e., path with exactly k - 1 edges and k vertices) in G, the two colors alternate along the P k , i.e., no two consecutive vertices of the P k belong to the same color V i , i = 1,2. Obviously, a graph is bipartite if and only if is P 2- bicolorable, every graph is P k -bicolorable for some k and if G is P k -bicolorable then it is P k + 1-bicolorable. The notion of P k -bicolorable graphs is motivated by a similar notion of cycle-bicolorable graphs introduced in connection with chordal probe graphs. Moreover, P 3- and P 4-bicolorable graphs are closely related to various other concepts such as 2-subcolorable graphs, P 4-bipartite graphs and alternately orientable graphs. We give a structural characterization of P 3-bicolorable graphs which also implies linear time recognition of these graphs. Moreover, we give a characterization of P 4-bicolorable graphs in terms of forbidden subgraphs.

Original languageEnglish
Title of host publicationGraph Theory, Computational Intelligence and Thought - Essays Dedicated to Martin Charles Golumbic on the Occasion of His 60th Birthday
EditorsMarina Lipshteyn, Vadim E. Levit, Ross M. McConnell
Number of pages11
StatePublished - 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5420 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


  • Bipartite graphs
  • Linear time recognition
  • P -bicolorable graphs
  • P -bicolorable graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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