Revisiting the Hamiltonian Theme in the Square of a Block: The General\n Case

2018/05/11 by Herbert Fleischner, Fleischner, Herbert, Gek L. Chia +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1805.04378

openalex publication_date 2018/05/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

This is the second part of joint research in which we show that every\n2-connected graph G has the cal F₄ property. That is, given distinct\nx_i\∈ V(G), 1\≤ i\≤ 4, there is an x₁x₂-hamiltonian path in G²\ncontaining different edges x₃y₃, x₄y₄\∈ E(G) for some y₃,y₄\∈ V(G).\nHowever, it was shown already in cite[Theorem 2]cf1:refer that 2-connected\nDT-graphs have the cal F₄ property; based on this result we generalize it\nto arbitrary 2-connected graphs. We also show that these results are best\npossible.\n

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