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The size of a hypergraph and its matching number
hypergraph its matching number Combinatorics
2011/9/22
Abstract: More than forty years ago, Erd\H{o}s conjectured that for any T <= N/K, every K-uniform hypergraph on N vertices without T disjoint edges has at most max{\binom{KT-1}{K}, \binom{N}{K} - \bin...
On the Eigenvalue Two and Matching Number of a Tree
Tree Laplacian eigenvalues matching number
2007/12/11
In [6], Guo and Tan have shown that $2$ is a Laplacianeigenvalue of any tree with perfect matchings. For trees withoutperfect matchings, we study whether $2$ is one of its Laplacianeigenvalues. If th...
A RELATION BETWEEN THE MATCHING NUMBER AND LAPLACIAN SPECTRUM OF A TREE
Tree Laplacian spectrum matching numbe
2007/8/7
Let $T$ be a tree with matching number $\mu(T)$. In this paper we obtain thefollowing result: If $T$ has no perfect matchings, then $\mu(T)$ is a lower bound forthe number of nonzero Laplacian eigenva...