Zobrazeno 1 - 10
of 85
pro vyhledávání: '"05C20, 05C35"'
Autor:
Cochran, Garner, Wang, Zhiyu
Erd\H{o}s, Pach, Pollack, and Tuza [J. Combin. Theory Ser. B, 47(1) (1989), 73--79] proved that the diameter of a connected $n$-vertex graph with minimum degree $\delta$ is at most $\frac{3n}{\delta+1}+O(1)$. The oriented diameter of an undirected gr
Externí odkaz:
http://arxiv.org/abs/2409.06587
Autor:
Stein, Maya, Trujillo-Negrete, Ana
We show that if $D$ is an $n$-vertex digraph with more than $(k-1)n$ arcs that does not contain any of three forbidden digraphs, then $D$ contains every antidirected tree on $k$ arcs. The forbidden digraphs are those orientations of $K_{2, \lceil k/1
Externí odkaz:
http://arxiv.org/abs/2404.10750
Autor:
Spiro, Sam
Given a digraph $D$, we say that a set of vertices $Q\subseteq V(D)$ is a $q$-kernel if $Q$ is an independent set and if every vertex of $D$ can be reached from $Q$ by a path of length at most $q$. In this paper, we initiate the study of several extr
Externí odkaz:
http://arxiv.org/abs/2404.07305
In a rainbow version of the classical Tur\'an problem one considers multiple graphs on a common vertex set, thinking of each graph as edges in a distinct color, and wants to determine the minimum number of edges in each color which guarantees existen
Externí odkaz:
http://arxiv.org/abs/2402.01028
Autor:
Yuster, Raphael
For every fixed $k \ge 4$, it is proved that if an $n$-vertex directed graph has at most $t$ pairwise arc-disjoint directed $k$-cycles, then there exists a set of at most $\frac{2}{3}kt+ o(n^2)$ arcs that meets all directed $k$-cycles and that the se
Externí odkaz:
http://arxiv.org/abs/2312.01901
One of the most fundamental results in graph theory is Mantel's theorem which determines the maximum number of edges in a triangle-free graph of order $n$. Recently a colorful variant of this problem has been solved. In such a variant we consider $c$
Externí odkaz:
http://arxiv.org/abs/2308.01461
Autor:
Grzesik, Andrzej, Jaworska, Justyna, Kielak, Bartłomiej, Novik, Aliaksandra, Ślusarczyk, Tomasz
A classical Tur\'an problem asks for the maximum possible number of edges in a graph of a given order that does not contain a particular graph $H$ as a subgraph. It is well-known that the chromatic number of $H$ is the graph parameter which describes
Externí odkaz:
http://arxiv.org/abs/2305.19959
Autor:
Chen, Bin, Hou, Xinmin
Let $\mathscr{H}$ be a family of digraphs. A digraph $D$ is \emph{$\mathscr{H}$-free} if it contains no isomorphic copy of any member of $\mathscr{H}$. For $k\geq2$, we set $C_{\leq k}=\{C_{2}, C_{3},\ldots,C_{k}\}$, where $C_{\ell}$ is a directed cy
Externí odkaz:
http://arxiv.org/abs/2211.03129
Autor:
Yuster, Raphael
Let $H$ be a directed acyclic graph other than a rooted star. It is known that there are constants $c(H)$ and $C(H)$ such that the following holds for the complete directed graph $D_n$. There are at most $C\log n$ directed acyclic subgraphs of $D_n$
Externí odkaz:
http://arxiv.org/abs/2205.10880
Autor:
Cambie, Stijn
Publikováno v:
J Graph Theory. 2021; 97:104-122
In 1984, Plesn\'{i}k determined the minimum total distance for given order and diameter and characterized the extremal graphs and digraphs. We prove the analog for given order and radius, when the order is sufficiently large compared to the radius. T
Externí odkaz:
http://arxiv.org/abs/2201.00185