On minimal triangle-free 6-chromatic graphs
نویسنده
چکیده
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 23 vertices and all triangle-free 5-chromatic graphs on 24 vertices with maximum degree at most 7. This implies that Reed’s conjecture holds for triangle-free graphs up to at least 24 vertices. Finally, we determine that the smallest regular trianglefree 5-chromatic graphs have 24 vertices.
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عنوان ژورنال:
- CoRR
دوره abs/1707.07581 شماره
صفحات -
تاریخ انتشار 2017