Add to ORKGIf a graph has bounded clique number and sufficiently large chromatic number, what can we say about its induced subgraphs? András Gyárfás made a number of challenging conjectures about this in the early 1980s, which have remained open until recently; but in the last few years there has been substantial progress. This is a survey of where we are now
Gyárfás conjectured in 1985 that for all k, ℓ, every graph with no clique of size more than k and no...
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertice...
Given a simple graph G = (V, E), a subset U of V is called a clique if it induces a complete subgrap...
If a graph has bounded clique number and sufficiently large chromatic number, what can we say about ...
We prove that, for every graph $F$ with at least one edge, there is a constant $c_F$ such that there...
A class of graphs is χ-bounded if there is a function such that χ(G)≤f(ω(G)) for every induced subgr...
International audienceA famous conjecture of Gyárfás and Sumner states for any tree T and integer k,...
International audienceA famous conjecture of Gyárfás and Sumner states for any tree T and integer k,...
We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of...
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic numb...
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic numb...
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic numb...
We prove a 1985 conjecture of Gyárfás that for all k, ℓ, every graph with sufficiently large chromat...
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic numb...
Gyárfás conjectured in 1985 that for all k, ℓ, every graph with no clique of size more than k and no...
Gyárfás conjectured in 1985 that for all k, ℓ, every graph with no clique of size more than k and no...
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertice...
Given a simple graph G = (V, E), a subset U of V is called a clique if it induces a complete subgrap...
If a graph has bounded clique number and sufficiently large chromatic number, what can we say about ...
We prove that, for every graph $F$ with at least one edge, there is a constant $c_F$ such that there...
A class of graphs is χ-bounded if there is a function such that χ(G)≤f(ω(G)) for every induced subgr...
International audienceA famous conjecture of Gyárfás and Sumner states for any tree T and integer k,...
International audienceA famous conjecture of Gyárfás and Sumner states for any tree T and integer k,...
We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of...
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic numb...
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic numb...
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic numb...
We prove a 1985 conjecture of Gyárfás that for all k, ℓ, every graph with sufficiently large chromat...
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic numb...
Gyárfás conjectured in 1985 that for all k, ℓ, every graph with no clique of size more than k and no...
Gyárfás conjectured in 1985 that for all k, ℓ, every graph with no clique of size more than k and no...
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertice...
Given a simple graph G = (V, E), a subset U of V is called a clique if it induces a complete subgrap...