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arXiv · 1501.04387

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

Nirmala Achuthan·N. R. Achuthan·G. Keady
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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 $χ_k(G)$ 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 $χ_k(G)$=m. In this paper we show that f(3,1;tfp)=11.

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Nirmala Achuthan, N. R. Achuthan, G. Keady. 2015-01-19. On minimal triangle-free planar graphs with prescribed 1-defective chromatic number. https://arxiv.org/abs/1501.04387

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