A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
ON SMALLEST ORDER OF TRIANGLE-FREE GRAPHS WITH PRESCRIBED (3, k)-DEFECTIVE CHROMATIC NUMBER

2018
*
Far East Journal of Mathematical Sciences (FJMS)
*

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 vertices receiving the same colour is at most k. The k-defective chromatic number Xk(G) of a graph G is the least positive integer m for which G is (m,k)-colourable. Let f(m,k) be the smallest order of a triangle-free graph G such that X k (G) = m. In this paper we study the problem of determining f( m, 1). We show that f(3, 1) = 9 and characterize the corresponding

doi:10.17654/ms103040717
fatcat:xpznpo5afrge7kb72pq3h7jvli