Kings in Multipartite Hypertournaments
Jiangdong Ai, Stefanie Gerke, Gregory Gutin
TL;DR
This paper investigates the existence of 4-kings in multipartite hypertournaments, proving one conjecture and providing counterexamples for the other, advancing understanding of dominance relations in complex hypergraph structures.
Contribution
It proves one of Petrovic's conjectures on 4-kings in multipartite hypertournaments and supplies counterexamples for the other, clarifying the conditions for kings in these structures.
Findings
Proved one conjecture on 4-kings in multipartite hypertournaments.
Provided counterexamples for the second conjecture.
Enhanced understanding of dominance properties in hypertournaments.
Abstract
In his paper "Kings in Bipartite Hypertournaments" (Graphs Combinatorics 35, 2019), Petrovic stated two conjectures on 4-kings in multipartite hypertournaments. We prove one of these conjectures and give counterexamples for the other.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory