论文标题
关于完整三方图的最佳取向
On optimal orientations of complete tripartite graphs
论文作者
论文摘要
给定一个连接且无用的图形$ g $，让$ \ mathscr {d}（g）$是$ g $的强向族的家族。 $ g $的方向数定义为$ \ bar {d}（g）：= min \ {d（d）| d \ in \ mathscr {d}（g）\} $，其中$ d（d（d）$是digraph $ d $的直径。在本文中，我们关注完整三方图的方向数量。我们证明了Rajasekaran和Sampathkumar提出的猜想。具体而言，对于$ q \ ge p \ ge 3 $，如果$ \ bar {d}（k（2，p，q））= 2 $，则$ q \ le {{p} \ select {\ lfloor {\ lfloor {p/2} \ rfloor}}} $。我们还向$ p $和$ q $呈现一些足够的条件，for $ \ bar {d}（k（p，p，q））= 2 $。
Given a connected and bridgeless graph $G$, let $\mathscr{D}(G)$ be the family of strong orientations of $G$. The orientation number of $G$ is defined to be $\bar{d}(G):=min\{d(D)|D\in \mathscr{D}(G)\}$, where $d(D)$ is the diameter of the digraph $D$. In this paper, we focus on the orientation number of complete tripartite graphs. We prove a conjecture raised by Rajasekaran and Sampathkumar. Specifically, for $q\ge p\ge 3$, if $\bar{d}(K(2,p,q))=2$, then $q\le{{p}\choose{\lfloor{p/2}\rfloor}}$. We also present some sufficient conditions on $p$ and $q$ for $\bar{d}(K(p,p,q))=2$.
