关于一致超图导出匹配可扩张性-基础数学专业毕业论文.pdfVIP

[19]. Inspired by those results, we intend to determine these properties about extendibility and IM- extendibility in hypergraphs, and some other properties (for example, the properties of the products) of them are also considered in this thesis. The followings are our main results: (1):If H is a r-uniform hypergraph with |X (H )| vertices, and let a positive integer n where n 2, Here, if |X (H )| is the multiple of r , and if H is an n-extendable hypergraph on |X (H )| vertices, then H is also (n − 1)-extendable. (2): If H is a n-extendable hypergrap, and H has no induced matching M with |M | n, then H is IM-extendable hypergraph. (3): If H is an IM-extendable hypergraph, and X ∗ ⊂ X, Y ∗ ⊂ X, X ∗ ∪ ∗ Y ∈ H, such that:d(x) = 2, d(y) = 2, then H ∗ ∗ is an IM-extendable. X \(X ∪Y ) (4): For every hypergraph H and every positive integer r , Kr is r- n uniform complete hypergraph , and n = rk , for a positive integer k, then H × Kr is IM-extendable. n (5): Suppose k1 and k2 are two positive integers and that the two hypergraphs H and H with H is k -extendable and H is k -extendable. 1 2 1 1 2 2 Then the product H1 × H2 is (k1 + k2 + 1)− extendable. Key words: hypergraphs matching induced matching extendable ex- tendibility IM-extendibility V ÆÆ 2006 0