Total coloring of rooted path graphs

Research output: Contribution to journalArticlepeer-review


A total coloring of a graph is an assignment of colors to both its vertices and edges so that adjacent or incident elements acquire distinct colors. In this note, we give a simple greedy algorithm to totally color a rooted path graph G with at most Δ(G)+2 colors, where Δ(G) is the maximum vertex degree of G. Our algorithm is inspired by a method by Bojarshinov (2001) [3] for interval graphs and provides a new proof that the Total Coloring Conjecture, posed independently by Behzad (1965) [1] and Vizing (1968) [15], holds for rooted path graphs. In the process, we also prove a useful property of greedy neighborhood coloring for chordal graphs.

Original languageEnglish
Pages (from-to)73-76
Number of pages4
JournalInformation Processing Letters
StatePublished - Jul 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.


  • Chordal graphs
  • Greedy neighborhood coloring
  • Rooted path graph
  • Total Coloring Conjecture
  • Total coloring

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


Dive into the research topics of 'Total coloring of rooted path graphs'. Together they form a unique fingerprint.

Cite this