On minimal triangle-free planar graphs with prescribed 1-defective chromatic number

Abstract

A graph is (m,k)-colourable if its vertices can be coloured with m colours such that the maximum degree of the subgraph induced on the set of all vertices receiving the same colour is at most k. The k-defective chromatic number ${\chi }_k(G)$ is the least positive integer $m$ for which graph G is (m,k)-colourable. Let f(m,k;tfp) be the smallest order of a triangle-free planar graph such that ${\chi }_k(G)$=m. In this paper we show that f(3,1;tfp)=11.

12pages, 5figures

References in corpus (1)

• On triangle-free graphs of order 10 with prescribed 1-defective chromatic number