On minimal trianglefree graphs with prescribed kdefective chromatic number
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Authors
Achuthan, Nirmala
Achuthan, Narasimaha
Simanihuruk, M.
Date
2011Type
Journal Article
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Achuthan, Nirmala and Achuthan, N.R. and Simanihuruk, M. 2011. On minimal trianglefree graphs with prescribed kdefective chromatic number. Discrete Mathematics. 311 (13): pp. 11191127.
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Discrete Mathematics
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School
Department of Mathematics and Statistics
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Abstract
A graph G is (m, k)colourable if its vertices can be coloured with m colours such that the maximum degree of any subgraph induced on vertices receiving the same colour is at most k. The kdefective chromatic number χk(G) is the least positive integer m for which G is (m, k)colourable. Let f(m, k) be the smallest order of a trianglefree graph such that χk(G)=m. In this paper we study the problem of determining f(m, k). We show that f(3, 2)=13 and characterize the corresponding minimal graphs. We present a lower bound for f(m, k) for all m≥3 and also an upper bound for f(3, k).
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