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On 2-colored graphs and partitions of boxes. (arXiv:1810.08920v1 [math.CO])
来源于:arXiv
We prove that if the edges of a graph G can be colored blue or red in such a
way that every vertex belongs to a monochromatic k-clique of each color, then G
has at least 4(k-1) vertices. This confirms a conjecture of Bucic, Lidicky,
Long, and Wagner (arXiv:1805.11278[math.CO]) and thereby solves the
2-dimensional case of their problem about partitions of discrete boxes with the
k-piercing property. We also characterize the case of equality in our result. 查看全文>>
