Zobrazeno 1 - 10
of 52
pro vyhledávání: '"05C20, 05C75"'
Autor:
Choi, Myungho, Kim, Suh-Ryung
We say that a digraph $D$ is $(i,j)$-step competitive if any two vertices have an $(i,j)$-step common out-neighbor in $D$ and that a graph $G$ is $(i,j)$-step competitively orientable if there exists an $(i,j)$-step competitive orientation of $G$. In
Externí odkaz:
http://arxiv.org/abs/2410.04379
The competition-common enemy graph (CCE graph) of a digraph $D$ is the graph with the vertex set $V(D)$ and an edge $uv$ if and only if $u$ and $v$ have a common predator and a common prey in $D$. If each vertex of a digraph $D$ has indegree at most
Externí odkaz:
http://arxiv.org/abs/2405.13363
Autor:
Chu, Hojin, Kim, Suh-Ryung
In this paper, we introduce the notion of two-way $(t,\lambda)$-liking digraphs as a way to extend the results for generalized friendship graphs. A two-way $(t,\lambda)$-liking digraph is a digraph in which every $t$ vertices have exactly $\lambda$ c
Externí odkaz:
http://arxiv.org/abs/2405.13293
Autor:
Choi, Myungho, Kim, Suh-Ryung
A multipartite tournament is an orientation of a complete $k$-partite graph for some positive integer $k\geq 3$. We say that a multipartite tournament $D$ is tight if every partite set forms a clique in the $(1,2)$-step competition graph, denoted by
Externí odkaz:
http://arxiv.org/abs/2402.01986
Autor:
Choi, Myungho, Kim, Suh-Ryung
A multipartite tournament is an orientation of a complete $k$-partite graph for some positive integer $k\geq 3$. We say that a multipartite tournament $D$ is tight if every partite set forms a clique in the $(1,2)$-step competition graph, denoted by
Externí odkaz:
http://arxiv.org/abs/2401.17817
In 1981, Bermond and Thomassen conjectured that for any positive integer $k$, every digraph with minimum out-degree at least $2k-1$ admits $k$ vertex-disjoint directed cycles. In this short paper, we verify the Bermond-Thomassen conjecture for triang
Externí odkaz:
http://arxiv.org/abs/2311.13369
Autor:
Duffy, Christopher
We consider the problem of classifying those graphs that arise as an undirected square of an oriented graph by generalising the notion of quasi-transitive directed graphs to mixed graphs. We fully classify those graphs of maximum degree three and tho
Externí odkaz:
http://arxiv.org/abs/2311.04429
The Friendship Theorem states that if in a party any pair of persons has precisely one common friend, then there is always a person who is everybody's friend and the theorem has been proved by Paul Erd\"{o}s, Alfr\'{e}d R\'{e}nyi, and Vera T. S\'{o}s
Externí odkaz:
http://arxiv.org/abs/2305.04058
Autor:
Choi, Myungho, Kim, Suh-Ryung
An acyclic digraph in which every vertex has indegree at most $i$ and outdegree at most $j$ is called an $(i,j)$ digraph for some positive integers $i$ and $j$. The phylogeny graph of a digraph $D$ has $V(D)$ as the vertex set and an edge $uv$ if and
Externí odkaz:
http://arxiv.org/abs/2212.05391
A major step in the graph minors theory of Robertson and Seymour is the transition from the Grid Theorem which, in some sense uniquely, describes areas of large treewidth within a graph, to a notion of local flatness of these areas in form of the exi
Externí odkaz:
http://arxiv.org/abs/2110.07553