Cliques in the Union of C4 -Free Graphs

Abeer Othman, Eli Berger

Research output: Contribution to journalArticlepeer-review


Let B and R be two simple C4-free graphs with the same vertex set V, and let B∨ R be the simple graph with vertex set V and edge set E(B) ∪ E(R). We prove that if B∨ R is a complete graph, then there exists a B-clique X, an R-clique Y and a set Z which is a clique both in B and in R, such that V= X∪ Y∪ Z. For general B and R, not necessarily forming together a complete graph, we obtain that ω(B∨R)≤ω(B)+ω(R)+12min(ω(B),ω(R))andω(B∨R)≤ω(B)+ω(R)+ω(B∧R)where B∧ R is the simple graph with vertex set V and edge set E(B) ∩ E(R).

Original languageEnglish
Pages (from-to)607-612
Number of pages6
JournalGraphs and Combinatorics
Issue number4
StatePublished - 1 Jul 2018

Bibliographical note

Funding Information:
This research is partially supported by the United States—Israel Binational Science Foundation Grants 2012031 and 2016077 and by Israel Science Foundation Grants 1581/12 and 936/16.

Publisher Copyright:
© 2018, Springer Japan KK, part of Springer Nature.


  • C-free graphs
  • Cliques
  • Obedient sets

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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