Turán Numbers of Subdivided Graphs

Turán Numbers for Disjoint Copies of Graphs

The Turán number ex(n,H) of H is the maximum number of edges of an n-vertex simple graph having no member ofH as a subgraph. We show lower and upper bounds for Turán numbers for disjoint copies of graphs.

A Note on Turán Numbers for Even Wheels

The Turán number ex(n,G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. We consider a very special case of the Simonovits’s theorem (Simonovits in: Theory of graphs, Academic Press, New York, 1968) which determine an asymptotic result for Turán numbers for graphs with some properties. In the paper we present a more precise result for even ...

Eternal m-security subdivision numbers in graphs

An eternal $m$-secure set of a graph $G = (V,E)$ is aset $S_0subseteq V$ that can defend against any sequence ofsingle-vertex attacks by means of multiple-guard shifts along theedges of $G$. A suitable placement of the guards is called aneternal $m$-secure set. The eternal $m$-security number$sigma_m(G)$ is the minimum cardinality among all eternal$m$-secure sets in $G$. An edge $uvin E(G)$ is ...

An Ordered Turán Problem for Bipartite Graphs

Let F be a graph. A graph G is F -free if it does not contain F as a subgraph. The Turán number of F , written ex(n, F ), is the maximum number of edges in an F -free graph with n vertices. The determination of Turán numbers of bipartite graphs is a challenging and widely investigated problem. In this paper we introduce an ordered version of the Turán problem for bipartite graphs. Let G be a gr...

Turán numbers of vertex-disjoint cliques in -partite graphs