Minimum degree distance among cacti with perfect matchings
نویسندگان
چکیده
منابع مشابه
Perfect matchings in uniform hypergraphs with large minimum degree
A perfect matching in a k-uniform hypergraph on n vertices, n divisible by k, is a set of n/k disjoint edges. In this paper we give a sufficient condition for the existence of a perfect matching in terms of a variant of the minimum degree. We prove that for every k ≥ 3 and sufficiently large n, a perfect matching exists in every n-vertex k-uniform hypergraph in which each set of k − 1 vertices ...
متن کاملExact minimum degree thresholds for perfect matchings in uniform hypergraphs
Article history: Received 19 August 2011 Available online xxxx Given positive integers k and where 4 divides k and k/2 k−1, we give a minimum -degree condition that ensures a perfect matching in a k-uniform hypergraph. This condition is best possible and improves on work of Pikhurko who gave an asymptotically exact result. Our approach makes use of the absorbing method, as well as the hypergrap...
متن کاملTight Minimum Degree Conditions Forcing Perfect Matchings in Uniform Hypergraphs
Given positive integers k and ` where k/2 ≤ ` ≤ k− 1, we give a minimum `-degree condition that ensures a perfect matching in a kuniform hypergraph. This condition is best possible and improves on work of Pikhurko [12] who gave an asymptotically exact result, and extends work of Rödl, Ruciński and Szemerédi [15] who determined the threshold for ` = k−1. Our approach makes use of the absorbing m...
متن کاملComputing Minimum-Weight Perfect Matchings
We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimum-weight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dual-change e for each tree. As a benchmark of t...
متن کاملThe degree resistance distance of cacti
Graph invariants, based on the distances between the vertices of a graph, are widely used in theoretical chemistry. The degree resistance distance of a graph G is defined as D R (G) = {u,v}⊆V (G) [d(u) + d(v)]R(u, v), where d(u) is the degree of the vertex u, and R(u, v) the resistance distance between the vertices u and v. Let Cact(n; t) be the set of all cacti possessing n vertices and t cy...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.01.005