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Kings in Multipartite Hypertournaments
Jiangdong Ai, Stefanie Gerke, Gregory Gutin
In his paper "Kings in Bipartite Hypertournaments" (Graphs Combinatorics 35, 2019), Petrovic stated two conjectures on 4-kings in multipartite hypertournaments. We prove one o…
Proximity and Remoteness in Directed and Undirected Graphs
Jiangdong Ai, Stefanie Gerke, Gregory Gutin +1
Let be a strongly connected digraph. The average distance of a vertex of is the arithmetic mean of the distances from to all other vertices of . The r…
Proper Orientation Number of Triangle-free Bridgeless Outerplanar Graphs
J. Ai, S. Gerke, G. Gutin +2
An orientation of is a digraph obtained from by replacing each edge by exactly one of two possible arcs with the same endpoints. We call an orientation \emph{proper} if nei…
k-Ary spanning trees contained in tournaments
Jiangdong Ai, Hui Lei, Yongtang Shi +2
A rooted tree is called a -ary tree, if all non-leaf vertices have exactly children, except possibly one non-leaf vertex has at most children. Denote by the min…