منابع مشابه
Average Degree Conditions Forcing a Minor
Mader first proved that high average degree forces a given graph as a minor. Often motivated by Hadwiger’s Conjecture, much research has focused on the average degree required to force a complete graph as a minor. Subsequently, various authors have considered the average degree required to force an arbitrary graph H as a minor. Here, we strengthen (under certain conditions) a recent result by R...
متن کاملun 2 01 5 Average degree conditions forcing a minor
Mader first proved that high average degree forces a given graph as a minor. Often motivated by Hadwiger’s Conjecture, much research has focused on the average degree required to force a complete graph as a minor. Subsequently, various authors have consider the average degree required to force an arbitrary graphH as a minor. Here, we strengthen (under certain conditions) a recent result by Reed...
متن کاملForcing k-blocks in graphs by minimum and average degree conditions
We investigate what conditions on the minimum or average degree of a graph ensure that it contains a k-block , a (maximal) set of at least k vertices no two of which can be separated by fewer than k vertices.
متن کاملForcing a sparse minor
This paper addresses the following question for a given graph H : what is the minimum number f(H) such that every graph with average degree at least f(H) contains H as a minor? Due to connections with Hadwiger’s Conjecture, this question has been studied in depth when H is a complete graph. Kostochka and Thomason independently proved that f(Kt) = ct √ ln t. More generally, Myers and Thomason de...
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...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5321