The Existence of Hamilton Cycle in n-Balanced k-Partite Graphs

2023/09/01 by Zongyuan Yang, Yi Zhang, Yang, Zongyuan +3
Mathematics · Computer Science · Engineering · #Limits and Structures in Graph Theory #Advanced Graph Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2309.00232

Abstract

Let G_k,n be the n-balanced k-partite graph, whose vertex set can be partitioned into k parts, each has n vertices. In this paper, we prove that if k ≥ 2,n ≥ 1, for the edge set E(G) of G_k,n |E(G)| ≥\1 · amp; \text if k=2, n=1 n² C_k²-(k-1) n+2 · amp; \text other . then G_k,n is hamiltonian. And the result may be the best.

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