Tight Chromatic Upper Bound for {3K1, C5}-free Graphs
Abstract
Problem of finding an optimal upper bound for a chromatic no. of 3K1-free graphs is still open and pretty hard. Here we find a tight chromatic upper bound for {3K1, C5}-free graphs. We prove that if G is {3K1, C5}-free, then the chromatic no. <= (3{\omega}-1)/2 where {\omega} is the size of a maximum clique in G and show with examples that the bound is tight.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2013
- DOI:
- 10.48550/arXiv.1307.0307
- arXiv:
- arXiv:1307.0307
- Bibcode:
- 2013arXiv1307.0307D
- Keywords:
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- Mathematics - Combinatorics;
- Math.CO
- E-Print:
- This paper has been withdrawn by the author as there is an exception to the theory