相关论文: The planar Turan number of double star S_(3,5)

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…

Given a graph $H,$ we say that a graph is \textit{$H$-free} if it does not contain $H$ as a subgraph. The Tur\'an number $\ex(n,H)$ of $H$ is the maximum number of edges in an $n$-vertex $H$-free graph, the set of all the corresponding…

Given a graph $H$, the Tur\'an number $ex(n,H)$ is the largest number of edges in an $H$-free graph on $n$ vertices. We make progress on a recent conjecture of Conlon, Janzer, and Lee on the Tur\'an numbers of bipartite graphs, which in…

Given a set of graphs $\mathcal{H}$, we say that a graph $G$ is \textit{$\mathcal{H}$-free} if it does not contain any member of $\mathcal{H}$ as a subgraph. Let $\text{ex}(n,\mathcal{H})$ (resp. $\text{ex}_{sp}(n,\mathcal{H})$) denote the…

The Tur\'an number $\text{ex}(n,H)$ of a graph $H$ is the maximal number of edges in an $H$-free graph on $n$ vertices. In $1983$ Chung and Erd\H{o}s asked which graphs $H$ with $e$ edges minimize $\text{ex}(n,H)$. They resolved this…

The $\textit{planar Tur\'an number}$ $\textrm{ex}_{\mathcal P}(n,H)$ of a graph $H$ is the maximum number of edges in an $n$-vertex planar graph without $H$ as a subgraph. Let $C_k$ denote the cycle of length $k$. The planar Tur\'an number…

The Tur\'{a}n number of a graph $H$, denoted $\mbox{ex}(n,H)$, is the maximum number of edges in an $n$-vertex graph with no subgraph isomorphic to $H$. Solymosi conjectured that if $H$ is any graph and $\mbox{ex}(n,H) = O(n^{\alpha})$…

The bipartite Tur\'{a}n number of a graph $H$, denoted by $ex(m,n; H)$, is the maximum number of edges in any bipartite graph $G=(X,Y; E)$ with $|X|=m$ and $|Y|=n$ which does not contain $H$ as a subgraph. In this paper, we determined…

For a family of graphs $\cal F$, a graph $G$ is $\cal F$-free if it does not contain a member of $\cal F$ as a subgraph. The Tur\'an number $\textrm{ex}(n,{\cal F})$ is the maximum number of edges in an $n$-vertex graph which is $\cal…

For a graph $H$, the {\em extremal number} $ex(n,H)$ is the maximum number of edges in a graph of order $n$ not containing a subgraph isomorphic to $H$. Let $\delta(H)>0$ and $\Delta(H)$ denote the minimum degree and maximum degree of $H$,…

A graph $G$ is rainbow-$F$-free if it admits a proper edge-coloring without a rainbow copy of $F$. The rainbow Tur\'an number of $F$, denoted $\mathrm{ex^*}(n,F)$, is the maximum number of edges in a rainbow-$F$-free graph on $n$ vertices.…

We determine the maximum possible number of edges of a graph with $n$ vertices, matching number at most $s$ and clique number at most $k$ for all admissible values of the parameters.

The Tur\'an number of a graph $H$, $\text{ex}(n,H)$, is the maximum number of edges in a graph on $n$ vertices which does not have $H$ as a subgraph. A wheel $W_n$ is an $n$-vertex graph formed by connecting a single vertex to all vertices…

We consider the Tur\'an problems of $2$-edge-colored graphs. A $2$-edge-colored graph $H=(V, E_r, E_b)$ is a triple consisting of the vertex set $V$, the set of red edges $E_r$ and the set of blue edges $E_b$ with $E_r$ and $E_b$ do not…

Let $\mathcal{F}$ denote a set of graphs. A graph $G$ is said to be $\mathcal{F}$-free if it does not contain any element of $\mathcal{F}$ as a subgraph. The Tur\'an number is the maximum possible number of edges in an $\mathcal{F}$-free…

The topological Tur\'an number $\mathrm{ex}_{\hom}(n,X)$ of a 2-dimensional simplicial complex $X$ asks for the maximum number of edges in an $n$-vertex 3-uniform hypergraph containing no triangulation of $X$ as a subgraph. We prove that…

Given a graph $H$ and a positive integer $n,$ the Tur\'{a}n number of $H$ for the order $n,$ denoted ${\rm ex}(n,H),$ is the maximum size of a simple graph of order $n$ not containing $H$ as a subgraph. The book with $p$ pages, denoted…

Given $r$-uniform hypergraphs $G$ and $H$ the Tur\'an number $\rm ex(G, H)$ is the maximum number of edges in an $H$-free subgraph of $G$. We study the typical value of $\rm ex(G, H)$ when $G=G_{n,p}^{(r)}$, the Erd\H{o}s-R\'enyi random…

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…

Given two graphs $H$ and $F$, the generalized Tur\'an number $\mathrm{ex}(n,H,F)$ is the largest number of copies of $H$ in an $n$-vertex $F$-free graph. For every $F$ and sufficiently large $n$, we present an extremal graph for a…