منابع مشابه
Forcing 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 کاملAverage 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 کاملStrongly-Bounded Sparse Decompositions of Minor Free Graphs
As networks grow large and complex, a key approach in managing information and constructing algorithms is to decompose the network into locality-preserving clusters. Then, information and/or management can be divided between the clusters, such that every node is responsible only for clusters for which it belongs. Such decompositions into locality sensitive clusters have become key tools in netw...
متن کامل$K_{4}$-Minor-Free Induced Subgraphs of Sparse Connected Graphs
We prove that every connected graph G with m edges contains a set X of at most 3 16 (m+ 1) vertices such that G−X has no K4 minor, or equivalently, has treewidth at most 2. This bound is best possible and improves a recent bound of 19 100m+ 3 20 due to Edwards and Farr. Connectivity is essential: If G is not connected then only a bound of 15m can be guaranteed.
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2015
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548315000073