In (J Graph Theory 33 (2000), 14-24), Hell and Zhu proved that if a series-parallel graph G has girth at least 2⌊(3k-1)/2⌋, then χc(G)≤4k/(2k-1). In (J Graph Theory 33 (2000), 185-198), Chien and Zhu proved that the girth condition given in (J Graph Theory 33 (2000), 14-24) is sharp. Short proofs of both results are given in this note.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-17716 |
| Date | 01 January 2011 |
| Creators | Holt, Tracy, Nigussie, Yared |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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