A mixed hypergraph is a triple H = (X; C;D), where X is the vertex set, and each of C;D is a list of subsets of X. A strict t-coloring is a onto mapping from X to {1, 2,…,t} such that each c belongs to C contains two vertices have a common value and each d belongs to D has two vertices have distinct values. If H has a strict t-coloring, then t belongs to S(H), such S(H) is called the feasible set of H, and k is a gap if there are a value larger than k and a value less than k in the feasible set but k is not.
We find the minimum and maximum gap of a mixed hypergraph with more than 5 vertices. Then we consider two special cases of the gap of mixed hypergraphs. First, if the mixed hypergraphs is spanned by a complete bipartite graph, then the gap is decided by the size of bipartition. Second, the (l,m)-uniform mixed hypergraphs has gaps if l > m/2 >2, and we prove that the minimum number of vertices of a (l,m)-uniform mixed hypergraph which has gaps is (m/2)( l -1) + m.
| Identifer | oai:union.ndltd.org:CHENGCHI/G0927510171 |
| Creators | 郭威廷, Kuo, Wei-Ting |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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