Related papers: On the Halin Tur\'an number of short cycles

The Tur\'an number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. Let P_k be the path with k vertices, the square P^2_k of P_k is obtained by joining the pairs of vertices…

A k-dimensional box is the Cartesian product R_1 x R_2 x ... x R_k where each R_i is a closed interval on the real line. The boxicity of a graph G, denoted as box(G) is the minimum integer k such that G is the intersection graph of a…

The planar Tur\'an number of a graph $H$, denoted by $ex_{_\mathcal{P}}(n,H)$, is the largest number of edges in a planar graph on $n $ vertices without containing $H$ as a subgraph. In this paper, we continue to study the topic of…

The Turan number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. We determine the Turan number and find the unique extremal graph for forests consisting of paths when n is…

The Tur\'{a}n number $ex(n,H)$ of a graph $H$ is the maximum number of edges in any $H$-free graph on $n$ vertices. The triangular pyramid of $k$-layers, denoted by $TP_k$, is a generalization of a triangle. The Tur\'an problems of a…

A graph $G$ of constant link $L$ is a graph in which the neighborhood of any vertex induces a graph isomorphic to $L$. Given two different graphs, $H$ and $G$, the induced Tur\'an number ${\rm ex}(n; H, G{\rm -ind})$ is defined as the…

Given a graph $L$, the Tur\'an number $\textrm{ex}(n,L)$ is the maximum possible number of edges in an $n$-vertex $L$-free graph. The study of Tur\'an number of graphs is a central topic in extremal graph theory. Although the celebrated…

Halin graphs constitute an interesting class of planar and polyhedral graphs. A generalized Halin graph is obtained by connecting all leaves of a planar embedding of a tree via a cycle. A Halin graph is a generalized Halin graph having no…

The Tur\'an number $ex(n,H)$ is the maximum number of edges in an $H$-free graph on $n$ vertices. Let $T$ be any tree. The odd-ballooning of $T$, denoted by $T_o$, is a graph obtained by replacing each edge of $T$ with an odd cycle…

Given a graph $F$, the Tur\'{a}n number ${\rm ex}(n,F)$ is the maximum number of edges in any $n$-vertex $F$-free graph. The odd-ballooning of $F$, denoted by $F^{o}$, is a graph obtained by replacing each edge of $F$ with an odd cycle,…

The planar Tur\'a number of a graph $F$ is the maximum number of edges an $n$-vertex $F$-free planar graph can have. We study the case where $F$ is forbidden as an induced subgraph, thereby introducing the induced planar Tur\'a numbers. We…

The {\em planar Tur\'{a}n number} of $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is the maximum number of edges in an $H$-free planar graph. The planar Tur\'{a}n number of $k\geq 3$ vertex-disjoint union of cycles is a trivial value $3n-6$.…

Let $\mathcal{F}$ be a set of graphs. The planar Tur\'an number, $ex_{\mathcal{P}}(n,\mathcal{F})$, is the maximum number of edges in an $n$-vertex planar graph which does not contain any member of $\mathcal{F}$ as a subgraph. In this…

For an $r$-uniform hypergraph $H$ and a family of $r$-uniform hypergraphs $\mathcal{F}$, the relative Tur\'{a}n number $\mathrm{ex}(H,\mathcal{F})$ is the maximum number of edges in an $\mathcal{F}$-free subgraph of $H$. In this paper we…

For a family of graphs $\mathcal{F}$, the Tur\'{a}n number $ex(n,\mathcal{F})$ is the maximum number of edges in an $n$-vertex graph containing no member of $\mathcal{F}$ as a subgraph. The maximum number of edges in an $n$-vertex connected…

As a variant of the much studied Tur\'an number, $ex(n,F)$, the largest number of edges that an $n$-vertex $F$-free graph may contain, we introduce the connected Tur\'an number $ex_c(n,F)$, the largest number of edges that an $n$-vertex…

For a connected labelled graph $G$, a {\em spanning tree} $T$ is a connected and an acyclic subgraph that spans all vertices of $G$. In this paper, we consider a classical combinatorial problem which is to list all spanning trees of $G$. A…

An ordered graph $H$ is a simple graph with a linear order on its vertex set. The corresponding Tur\'an problem, first studied by Pach and Tardos, asks for the maximum number $\text{ex}_<(n,H)$ of edges in an ordered graph on $n$ vertices…

The Tur\'an number of a graph $H$, denoted by $ex(n, H)$, is the maximum number of edges in any graph on $n$ vertices containing no $H$ as a subgraph. Let $P_k$ denote the path on $k$ vertices, $S_k$ denote the star on $k+1$ vertices and…

An $r$-graph is an $r$-uniform hypergraph tree (or $r$-tree) if its edges can be ordered as $E_1,\ldots, E_m$ such that $\forall i>1 \, \exists \alpha(i)<i$ such that $E_i\cap (\bigcup_{j=1}^{i-1} E_j)\subseteq E_{\alpha(i)}$. The Tur\'an…