# Conditions for $\beta$-perfectness

J.C.M. Keijsper, M. Tewes

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## Abstract

A $\beta$-perfect graph is a simple graph $G$ such that $\chi(G')=\beta(G')$ for every induced subgraph $G'$ of $G$, where $\chi(G')$ is the chromatic number of $G'$, and $\beta(G')$ is defined as the maximum over all induced subgraphs $H$ of $G'$ of the minimum vertex degree in $H$. The vertices of a $\beta$-perfect graph $G$ can be coloured with $\chi(G)$ colours in polynomial time (greedily).
Original language Undefined Enschede University of Twente, Department of Applied Mathematics Published - 2000

### Publication series

Name Department of Applied Mathematics, University of Twente 1537 0169-2690

• EWI-3357
• MSC-05C75
• MSC-05C15
• IR-65724