Semi-balanced colorings of graphs: Generalized 2-colorings based on a relaxed discrepancy condition

Jesper Jansson, Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We generalize the concept of a 2-coloring of a graph to what we call a semi-balanced coloring by relaxing a certain discrepancy condition on the shortest-paths hypergraph of the graph. Let G be an undirected, unweighted, connected graph with n vertices and m edges. We prove that the number of different semi-balanced colorings of G is: (1) at most n + 1 if G is bipartite; (2) at most m if G is non-bipartite and triangle-free; and (3) at most m + 1 if G is non-bipartite. Based on the above combinatorial investigation, we design an algorithm to enumerate all semi-balanced colorings of G in O(nm2) time.

Original languageEnglish
Pages (from-to)205-222
Number of pages18
JournalGraphs and Combinatorics
Volume20
Issue number2
DOIs
Publication statusPublished - 2004 Dec 1

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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