Perfect Matchings, Tilings and Hamilton Cycles in Hypergraphs
نویسندگان
چکیده
This thesis contains problems in finding spanning subgraphs in graphs, such as, perfect matchings, tilings and Hamilton cycles. First, we consider the tiling problems in graphs, which are natural generalizations of the matching problems. We give new proofs of the multipartite Hajnal-Szemerédi Theorem for the tripartite and quadripartite cases. Second, we consider Hamilton cycles in hypergraphs. In particular, we determine the minimum codegree thresholds for Hamilton `-cycles in large k-uniform hypergraphs for ` < k/2. We also determine the minimum vertex degree threshold for loose Hamilton cycle in large 3-uniform hypergraphs. These results generalize the well-known theorem of Dirac for
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