Add to ORKGHadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. Let G be a graph on n vertices with chromatic number χ and stability number α. Then since χα ≥ n, Hadwiger’s conjecture implies that G has a clique minor of size n α. In this paper we prove that this is true for connected claw-free graphs with α ≥ 3. We also show that this result is tight by providing an infinite family of claw-free graphs with α ≥ 3 that do not have a clique minor of size larger than n
Graph theory is the study of graphs that represent a specific relation between pairs of objects from...
The Hadwiger number h(G) of a graph G is the maximum integer t such that K-t is a minor of G. Since ...
We introduce the following weak version of Hadwiger's conjecture: If G is a graph and is a cardinal...
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. ...
AbstractHadwigerʼs conjecture states that every graph with chromatic number χ has a clique minor of ...
The classical Hadwiger conjecture dating back to 1940s states that any graph of chromatic number at ...
AbstractA weakening of Hadwiger’s conjecture states that every n-vertex graph with independence numb...
Abstract Let G be a graph with n vertices and independence number α. Hadwiger's conjecture impl...
Given a graph G, the Hadwiger number of G, denoted by h(G), is the largest integer κ such that G con...
The Hadwiger number h(G) of a graph G is the maximum size of a complete minor of G. Hadwiger's Conje...
AbstractWe investigate Hadwiger's conjecture for graphs with no stable set of size 3. Such a graph o...
The Hadwiger number h(G) of a graph G is the maximum integer f such that Kt is a minor of G. Since ξ...
Hadwiger\u27s conjecture from 1943 states that for every integer t≥1, every graph either can be t-co...
The Hadwiger number $\eta(G)$ of a graph G is the largest integer h such that the complete graph on ...
AbstractThe main result of this paper is the following: Any minimal counterexample to Hadwiger's Con...
Graph theory is the study of graphs that represent a specific relation between pairs of objects from...
The Hadwiger number h(G) of a graph G is the maximum integer t such that K-t is a minor of G. Since ...
We introduce the following weak version of Hadwiger's conjecture: If G is a graph and is a cardinal...
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. ...
AbstractHadwigerʼs conjecture states that every graph with chromatic number χ has a clique minor of ...
The classical Hadwiger conjecture dating back to 1940s states that any graph of chromatic number at ...
AbstractA weakening of Hadwiger’s conjecture states that every n-vertex graph with independence numb...
Abstract Let G be a graph with n vertices and independence number α. Hadwiger's conjecture impl...
Given a graph G, the Hadwiger number of G, denoted by h(G), is the largest integer κ such that G con...
The Hadwiger number h(G) of a graph G is the maximum size of a complete minor of G. Hadwiger's Conje...
AbstractWe investigate Hadwiger's conjecture for graphs with no stable set of size 3. Such a graph o...
The Hadwiger number h(G) of a graph G is the maximum integer f such that Kt is a minor of G. Since ξ...
Hadwiger\u27s conjecture from 1943 states that for every integer t≥1, every graph either can be t-co...
The Hadwiger number $\eta(G)$ of a graph G is the largest integer h such that the complete graph on ...
AbstractThe main result of this paper is the following: Any minimal counterexample to Hadwiger's Con...
Graph theory is the study of graphs that represent a specific relation between pairs of objects from...
The Hadwiger number h(G) of a graph G is the maximum integer t such that K-t is a minor of G. Since ...
We introduce the following weak version of Hadwiger's conjecture: If G is a graph and is a cardinal...