Add to ORKGInternational audienceA Kl-expansion consists of l vertex-disjoint trees, every two of which are joined by an edge. We call such an expansion odd if its vertices can be two-coloured so that the edges of the trees are bichromatic but the edges between trees are monochromatic. We show that, for every l, if a graph contains no odd Kl-expansion then its chromatic number is View the MathML source. In doing so, we obtain a characterization of graphs which contain no odd Kl-expansion which is of independent interest. We also prove that given a graph and a subset S of its vertex set, either there are k vertex-disjoint odd paths with endpoints in S, or there is a set X of at most 2kâˆ'2 vertices such that every odd path with both ends in S contains ...
AbstractAssuming that a graph G on n vertices is a minimal counterexample to Hadwiger's Conjecture χ...
We propose local versions of Hadwiger's Conjecture, where only balls of radius $\Omega(\log v(G))$ a...
AbstractIf G is a graph with k ⩾ 1 odd cycle lengths then each block of G is either K2k+2 or contain...
International audienceA Kl-expansion consists of l vertex-disjoint trees, every two of which are joi...
AbstractA Kl-expansion consists of l vertex-disjoint trees, every two of which are joined by an edge...
We say that H has an odd complete minor of order at least l if there are l vertex disjoint trees in ...
AbstractWe give a short proof that every graph G without an odd Kk-minor is O(klogk)-colorable. This...
Motivated by different characterizations of planar graphs and the 4-Color Theorem, several structura...
Hadwiger’s Conjecture asserts that every Kt-minor-free graph has a proper (t − 1)-colouring. We rela...
AbstractGerards and Seymour (see [T.R. Jensen, B. Toft, Graph Coloring Problems, Wiley-Interscience,...
AbstractConsider the following relaxation of the Hadwiger Conjecture: For each t there exists Nt suc...
In 1943, Hadwiger conjectured that every graph with no $K_t$ minor is $(t-1)$-colorable for every $t...
Graph theory is the study of graphs that represent a specific relation between pairs of objects from...
Let $h(G)$ denote the largest $t$ such that $G$ contains $K_t$ as a minor, $\chi(G)$ the chromatic n...
Given a graph G, the Hadwiger number of G, denoted by h(G), is the largest integer κ such that G con...
AbstractAssuming that a graph G on n vertices is a minimal counterexample to Hadwiger's Conjecture χ...
We propose local versions of Hadwiger's Conjecture, where only balls of radius $\Omega(\log v(G))$ a...
AbstractIf G is a graph with k ⩾ 1 odd cycle lengths then each block of G is either K2k+2 or contain...
International audienceA Kl-expansion consists of l vertex-disjoint trees, every two of which are joi...
AbstractA Kl-expansion consists of l vertex-disjoint trees, every two of which are joined by an edge...
We say that H has an odd complete minor of order at least l if there are l vertex disjoint trees in ...
AbstractWe give a short proof that every graph G without an odd Kk-minor is O(klogk)-colorable. This...
Motivated by different characterizations of planar graphs and the 4-Color Theorem, several structura...
Hadwiger’s Conjecture asserts that every Kt-minor-free graph has a proper (t − 1)-colouring. We rela...
AbstractGerards and Seymour (see [T.R. Jensen, B. Toft, Graph Coloring Problems, Wiley-Interscience,...
AbstractConsider the following relaxation of the Hadwiger Conjecture: For each t there exists Nt suc...
In 1943, Hadwiger conjectured that every graph with no $K_t$ minor is $(t-1)$-colorable for every $t...
Graph theory is the study of graphs that represent a specific relation between pairs of objects from...
Let $h(G)$ denote the largest $t$ such that $G$ contains $K_t$ as a minor, $\chi(G)$ the chromatic n...
Given a graph G, the Hadwiger number of G, denoted by h(G), is the largest integer κ such that G con...
AbstractAssuming that a graph G on n vertices is a minimal counterexample to Hadwiger's Conjecture χ...
We propose local versions of Hadwiger's Conjecture, where only balls of radius $\Omega(\log v(G))$ a...
AbstractIf G is a graph with k ⩾ 1 odd cycle lengths then each block of G is either K2k+2 or contain...