Colouring H-Free Graphs of Bounded Diameter

Authors Barnaby Martin, Daniël Paulusma, Siani Smith

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Barnaby Martin
  • Department of Computer Science, Durham University, United Kingdom
Daniël Paulusma
  • Department of Computer Science, Durham University, United Kingdom
Siani Smith
  • Department of Computer Science, Durham University, United Kingdom

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Barnaby Martin, Daniël Paulusma, and Siani Smith. Colouring H-Free Graphs of Bounded Diameter. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


The Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for an integer k, such that no two adjacent vertices are coloured alike. A graph G is H-free if G does not contain H as an induced subgraph. It is known that Colouring is NP-complete for H-free graphs if H contains a cycle or claw, even for fixed k >= 3. We examine to what extent the situation may change if in addition the input graph has bounded diameter.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • vertex colouring
  • H-free graph
  • diameter


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