Cost Total Colorings of Trees

Shuji Isobe, Xiao Zhou, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


A total coloring of a graph G is to color all vertices and edges of G so that no two adjacent or incident elements receive the same color. Let C be a set of colors, and let ω be a cost function which assigns to each color c in C a real number ω(c) as a cost of c. A total coloring f of G is called an optimal total coloring if the sum of costs ω(f(x)) of colors f(x) assigned to all vertices and edges x is as small as possible. In this paper, we give an algorithm to find an optimal total coloring of any tree T in time O(nΔ3) where n is the number of vertices in T and Δ is the maximum degree of T.

Original languageEnglish
Pages (from-to)337-342
Number of pages6
JournalIEICE Transactions on Information and Systems
Issue number2
Publication statusPublished - 2004 Feb


  • Cost total coloring
  • Dynamic programming
  • Matching
  • Total coloring
  • Tree

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence


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