3一致反超图的完全不规则嵌入

Totaly Irregular Embedding of Co-hypergraphs

众所周知,任意顶点数大于1的图至少有两个点的度数相同。但该结论对反超图不再成立。证明了任意3一致反超图都可嵌入到一个完全不规则3一致反超图中,且保持上色数不变,从而也证明了完全不规则反超图的存在性。

Every graph has at least two vertices of same degree. But it not true for cohypergraphs. This paper proves that every 3uniform cohypergraphs, H1, can be embedded into a totaly irregular 3uniform cohypergraphs, H, with (H1)=(H). This result also guarantees the existence of a totaly irregular cohypergraphs.