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- W2736331343 abstract "A graph with chromatic number $k$ is called $k$-chromatic. Using computational methods, we show that the smallest triangle-free 6-chromatic graphs have at least 32 and at most 40 vertices. We also determine the complete set of all triangle-free 5-chromatic graphs up to 24 vertices. This implies that Reed's conjecture holds for triangle-free graphs up to at least this order. We also establish that the smallest regular triangle-free 5-chromatic graphs have 24 vertices. Finally, we show that the smallest 5-chromatic graphs of girth at least 5 have at least 29 vertices and that the smallest 4-chromatic graphs of girth at least 6 have at least 25 vertices." @default.
- W2736331343 created "2017-07-31" @default.
- W2736331343 creator A5057847156 @default.
- W2736331343 date "2017-07-24" @default.
- W2736331343 modified "2023-09-27" @default.
- W2736331343 title "On minimal triangle-free 6-chromatic graphs" @default.
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