Add to ORKGConsider a graph G on n vertices with α (n 2) edges which does not contain an induced K2,t (t ⩾ 2). How large must α be to ensure that G contains, say, a large clique or some fixed subgraph H? We give results for two regimes: for α bounded away from zero and for α = o(1). Our results for α = o(1) are strongly related to the Induced Tur´an numbers which were recently introduced by Loh, Tait, Timmons and Zhou. For α bounded away from zero, our results can be seen as a generalisation of a result of Gyárfás, Hubenko and Solymosi and more recently Holmsen (whose argument inspired ours
AbstractWe consider the following problem as a generalization of that solved by Tura´n's theorem. Le...
AbstractFor a graph G, let t(G) denote the maximum number of vertices in an induced subgraph of G th...
We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of...
Consider a graph G on n vertices with αn 2 edges which does not contain an induced K2,t (t > 2). How...
AbstractFor a graph G, let t(G) denote the maximum number of vertices in an induced subgraph of G th...
A subgraph of a graph G is called trivial if it is either a clique or an independent set. Let q(G) ...
AbstractThe main aim of the paper is to show that for 2⩽r<s and large enough n, there are graphs of ...
We prove that, for every graph $F$ with at least one edge, there is a constant $c_F$ such that there...
The inducibility of a graph H measures the maximum number of induced copies of H a large graph G can...
Brooks ’ Theorem implies that if a graph has ∆ ≥ 3 and and χ> ∆, then ω = ∆+1. Borodin and Kosto...
If a graph has bounded clique number and sufficiently large chromatic number, what can we say about ...
Ramsey’s theorem says that for every clique H1 and for every graph H2 with no edges, all graphs cont...
The following very natural problem was raised by Chung and Erdős in the early 80’s and has since bee...
The final publication is available at Elsevier via https://doi.org/10.1016/j.jctb.2022.09.001 © 2023...
In this note, extending some results of Erdö;s, Frankl, Rödl, Alexeev, Bollobás and Thomason, we det...
AbstractWe consider the following problem as a generalization of that solved by Tura´n's theorem. Le...
AbstractFor a graph G, let t(G) denote the maximum number of vertices in an induced subgraph of G th...
We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of...
Consider a graph G on n vertices with αn 2 edges which does not contain an induced K2,t (t > 2). How...
AbstractFor a graph G, let t(G) denote the maximum number of vertices in an induced subgraph of G th...
A subgraph of a graph G is called trivial if it is either a clique or an independent set. Let q(G) ...
AbstractThe main aim of the paper is to show that for 2⩽r<s and large enough n, there are graphs of ...
We prove that, for every graph $F$ with at least one edge, there is a constant $c_F$ such that there...
The inducibility of a graph H measures the maximum number of induced copies of H a large graph G can...
Brooks ’ Theorem implies that if a graph has ∆ ≥ 3 and and χ> ∆, then ω = ∆+1. Borodin and Kosto...
If a graph has bounded clique number and sufficiently large chromatic number, what can we say about ...
Ramsey’s theorem says that for every clique H1 and for every graph H2 with no edges, all graphs cont...
The following very natural problem was raised by Chung and Erdős in the early 80’s and has since bee...
The final publication is available at Elsevier via https://doi.org/10.1016/j.jctb.2022.09.001 © 2023...
In this note, extending some results of Erdö;s, Frankl, Rödl, Alexeev, Bollobás and Thomason, we det...
AbstractWe consider the following problem as a generalization of that solved by Tura´n's theorem. Le...
AbstractFor a graph G, let t(G) denote the maximum number of vertices in an induced subgraph of G th...
We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of...