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The niche graph of a digraph $D$ has $V(D)$ as the vertex set and an edge $uv$ if and only if $(u,w) \in A(D)$ and $(v,w) \in A(D)$, or $(w,u) \in A(D)$ and $(w,v) \in A(D)$ for some $w \in V(D)$. The notion of niche graph was introduced by Cable et
Externí odkaz:
http://arxiv.org/abs/1911.04191
For a positive integer $p$, the $p$-competition graph of a digraph $D$ is a graph which has the same vertex set as $D$ and an edge between distinct vertices $x$ and $y$ if and only if $x$ and $y$ have at least $p$ common out-neighbors in $D$. A graph
Externí odkaz:
http://arxiv.org/abs/1905.10966
Given an acyclic digraph $D$, the competition graph of $D$, denoted by $C(D)$, is the simple graph having vertex set $V(D)$ and edge set $\{uv \mid (u, w), (v, w) \in A(D) \text{ for some } w \in V(D) \}$. The phylogeny graph of an acyclic digraph $D
Externí odkaz:
http://arxiv.org/abs/1904.07420
Autor:
Eoh, Soogang, Kim, Suh-Ryung
In this paper, we introduce the notion of the weak majority dimension of a digraph which is well-defined for any digraph. We first study properties shared by the weak dimension of a digraph and show that a weak majority dimension of a digraph can be
Externí odkaz:
http://arxiv.org/abs/1903.09933
In this paper, we completely characterize the $m$-step competition graph of a bipartite tournament for any integer $m \ge 2$. In addition, we compute the competition index and the competition period of a bipartite tournament.
Externí odkaz:
http://arxiv.org/abs/1903.05332
Autor:
Eoh, Soogang, Kim, Suh-Ryung
An acyclic digraph each vertex of which has indegree at most $i$ and outdegree at most $j$ is called an $(i, j)$ digraph for some positive integers $i$ and $j$. Lee {\it et al.} (2017) studied the phylogeny graphs of $(2, 2)$ digraphs and gave suffic
Externí odkaz:
http://arxiv.org/abs/1810.11982
In this paper, we completely characterize the niche graphs of bipartite tournaments and find their interesting properties.
Externí odkaz:
http://arxiv.org/abs/1810.05279
In this paper, we present a minimal chordal completion $G^*$ of a graph $G$ satisfying the inequality $\omega(G^*) - \omega(G) \le i(G)$ for the non-chordality index $i(G)$ of $G$. In terms of our chordal completions, we partially settle the Hadwiger
Externí odkaz:
http://arxiv.org/abs/1810.05280
In this paper, we use the Erd\"{o}s-Szekeres lemma to show that there exists a graph with partial order competition dimension greater than five.
Externí odkaz:
http://arxiv.org/abs/1810.05278