Add to ORKGWe show that for every odd integer g 5 there exists a constant c such that every graph of minimum degree r and girth at least g contains a minor of minimum degree at least cr . This is best possible up to the value of the constant c for g = 5; 7 and 11. More generally, a wellknown conjecture about the minimal order of graphs of given minimum degree and large girth would imply that our result gives the correct order of magnitude for all odd values of g. The case g = 5 of our result implies Hadwiger's conjecture for C 4 -free graphs of suciently large chromatic number
AbstractMyers conjectured that for every integer s there exists a positive constant C such that for ...
We show that if G is a graph on n vertices, with all degrees comparable to some d = d(n), and withou...
AbstractWe prove that every graph of minimum degree at least r and girth at least 186 contains a sub...
The classical Hadwiger conjecture dating back to 1940s states that any graph of chromatic number at ...
Abstract. We study minimum degree conditions for which a graph with given odd girth has a simple str...
AbstractLet H be a fixed graph. We show that any H-minor free graph G of high enough girth has circu...
A graph H is a minor of another graph G, denoted by $H\ {\prec\sb{m}}\ G,$ if a graph isomorphic to ...
A graph H is a minor of another graph G, denoted by $H\ {\prec\sb{m}}\ G,$ if a graph isomorphic to ...
Abstract Let G be a graph with n vertices and independence number α. Hadwiger's conjecture impl...
This paper addresses the following question for a given graph H: What is the minimum number f(H) suc...
Abstract. A fundamental result in structural graph theory states that every graph with large average...
A fundamental result of Mader from 1972 asserts that a graph of high average degree contains a highl...
Mader proved that for every integer t there is a smallest real number c(t) such that any graph with ...
We say that H has an odd complete minor of order at least l if there are l vertex disjoint trees in ...
We say that H has an odd complete minor of order at least l if there are l vertex disjoint trees in ...
AbstractMyers conjectured that for every integer s there exists a positive constant C such that for ...
We show that if G is a graph on n vertices, with all degrees comparable to some d = d(n), and withou...
AbstractWe prove that every graph of minimum degree at least r and girth at least 186 contains a sub...
The classical Hadwiger conjecture dating back to 1940s states that any graph of chromatic number at ...
Abstract. We study minimum degree conditions for which a graph with given odd girth has a simple str...
AbstractLet H be a fixed graph. We show that any H-minor free graph G of high enough girth has circu...
A graph H is a minor of another graph G, denoted by $H\ {\prec\sb{m}}\ G,$ if a graph isomorphic to ...
A graph H is a minor of another graph G, denoted by $H\ {\prec\sb{m}}\ G,$ if a graph isomorphic to ...
Abstract Let G be a graph with n vertices and independence number α. Hadwiger's conjecture impl...
This paper addresses the following question for a given graph H: What is the minimum number f(H) suc...
Abstract. A fundamental result in structural graph theory states that every graph with large average...
A fundamental result of Mader from 1972 asserts that a graph of high average degree contains a highl...
Mader proved that for every integer t there is a smallest real number c(t) such that any graph with ...
We say that H has an odd complete minor of order at least l if there are l vertex disjoint trees in ...
We say that H has an odd complete minor of order at least l if there are l vertex disjoint trees in ...
AbstractMyers conjectured that for every integer s there exists a positive constant C such that for ...
We show that if G is a graph on n vertices, with all degrees comparable to some d = d(n), and withou...
AbstractWe prove that every graph of minimum degree at least r and girth at least 186 contains a sub...