Following [1] , we investigate the problem of covering a graph G with induced subgraphs G 1 ; . . . ; G k of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciprocals of the chromatic numbers of the G i 's containing u is at least 1. The existence of such ''ch
✦ LIBER ✦
A Graph with cover degeneracy less than chromatic number
✍ Scribed by A.V. Pyatkin
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 78 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0364-9024
- DOI
- 10.1002/jgt.1019
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✦ Synopsis
Abstract
This note contains an example of a 4‐chromatic graph which admits a vertex partition into three parts such that the union of every two of them induces a forest. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 243–246, 2001
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## Abstract In this article we give examples of a triangle‐free graph on 22 vertices with chromatic number 5 and a __K__~4~‐free graph on 11 vertices with chromatic number 5. We very briefly describe the computer searches demonstrating that these are the smallest possible such graphs. All 5‐critica