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For a ‐uniform hypergraph , let denote the minimum vertex degree of , and denote the size of the largest matching in . In this paper, we show that for any and , there exists an integer such that for positive integers and ...
Let G be a graph and f an integer-valued function on V(G). Let h be a function that assigns each edge to a number in [0,1], such that the f-fractional number of G is the supremum of ∑e∈E(G)h(e) over all fractional functions h satisfying ∑e∼vh(e)≤f(v) for every vertex v∈V(G). An f-fractional factor is a spanning subgraph such that ∑v∼eh(e)=f(v) for every vertex v. In this work, we provide a new formula...
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