相关论文: On the Erd\H{o}s-Hajnal conjecture for six-vertex …

A celebrated unresolved conjecture of Erd\"{o}s and Hajnal states that for every undirected graph $H$ there exists $ \epsilon(H) > 0 $ such that every undirected graph on $ n $ vertices that does not contain $H$ as an induced subgraph…

A celebrated unresolved conjecture of Erd\"{o}s and Hajnal states that for every undirected graph $H$ there exists $ \epsilon(H) > 0 $ such that every undirected graph on $ n $ vertices that does not contain $H$ as an induced subgraph…

The celebrated Erd\"{o}s-Hajnal conjecture states that for every undirected graph $H$ there exists $ \epsilon(H) > 0 $ such that every undirected graph on $ n $ vertices that does not contain $H$ as an induced subgraph contains a clique or…

Erd\"{o}s-Hajnal conjecture states that for every undirected graph $H$ there exists $ \epsilon(H) > 0 $ such that every undirected graph on $ n $ vertices that does not contain $H$ as an induced subgraph contains a clique or a stable set of…

The Erd\H{o}s-Hajnal Conjecture states that for every $H$ there exists a constant $\epsilon(H)>0$ such that every graph $G$ that does not contain $H$ as an induced subgraph contains a clique or a stable set of size at least…

The Erd\H{o}s-Hajnal conjecture states that for every given undirected graph $H$ there exists a constant $c(H)>0$ such that every graph $G$ that does not contain $H$ as an induced subgraph contains a clique or a stable set of size at least…

A conjecture of Alon, Pach and Solymosi, which is equivalent to the celebrated Erd\H{o}s-Hajnal Conjecture, states that for every tournament $S$ there exists $\epsilon(S)>0$ such that if $T$ is an $n$-vertex tournament that does not…

We prove that there exists $C>0$ such that $\epsilon(H) \geq \frac{C}{|H|^{5}\log(|H|)}$, where $\epsilon(H)$ is the Erd\H{o}s-Hajnal coefficient of the tournament $H$, for every prime tournament $H$ for which the celebrated…

An equivalent directed version of the celebrated unresolved conjecture of Erdos and Hajnal proposed by Alon, Pack, and Solymosi states that for every tournament H there exists epsilon(H)>0 such that every H-free n-vertex tournament T…

An equivalent directed version of the celebrated unresolved conjecture of Erdos and Hajnal proposed by Alon et al. states that for every tournament H there exists epsilon(H) > 0 such that every H-free n-vertex tournament T contains a…

Erd\H{o}s and Hajnal conjectured that for every graph $H$, there exists $c>0$ such that every $H$-free graph $G$ has a clique or a stable set of size at least $|G|^c$ (a graph is $H$-free if it has no induced subgraph isomorphic to $H$).…

The Erd\H{o}s-Hajnal conjecture is one of the most classical and well-known problems in extremal and structural combinatorics dating back to 1977. It asserts that in stark contrast to the case of a general $n$-vertex graph if one imposes…

The Erd\H{o}s-Hajnal conjecture says that, for every graph $H$, there exists $c>0$ such that every $H$-free graph on $n$ vertices has a clique or stable set of size at least $n^c$. In this paper we are concerned with the case when $H$ is a…

A pure pair in a tournament $G$ is an ordered pair $(A,B)$ of disjoint subsets of $V(G)$ such that every vertex in $B$ is adjacent from every vertex in $A$. Which tournaments $H$ have the property that if $G$ is a tournament not containing…

The Erd\"os-Hajnal conjecture states that for every graph $H$, there exists a constant $\delta(H) > 0$ such that every graph $G$ with no induced subgraph isomorphic to $H$ has either a clique or a stable set of size at least…

We prove that for every graph $H$, there exists $\varepsilon>0$ such that every $n$-vertex graph with no vertex-minors isomorphic to $H$ has a pair of disjoint sets $A$, $B$ of vertices such that $|A|, |B|\ge \varepsilon n$ and $A$ is…

In this thesis we prove a variety of theorems on tournaments. A \emph{prime} tournament is a tournament $G$ such that there is no $X \subseteq V(G)$, $1 < |X| < |V(G)|$, such that for every vertex $v \in V(G) \minus X$, either $v \ra x$ for…

The Erdos-Hajnal conjecture says that for every graph H there exists c>0 such that every graph G not containing H as an induced subgraph has a clique or stable set of cardinality at least |G|^c. We prove that this is true when H is a cycle…

We prove the Erd\H{o}s-Hajnal conjecture for the five-vertex path $P_5$; that is, there exists $c>0$ such that every $n$-vertex graph with no induced $P_5$ has a clique or stable set of size at least $n^c$. This completes the verification…

Erd\H{o}s and Hajnal conjectured that, for every graph $H$, there exists a constant $c_H$ such that every graph $G$ on $n$ vertices which does not contain any induced copy of $H$ has a clique or a stable set of size $n^{c_H}$. We prove that…