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A NOTE ON MINIMUM DEGREE, BIPARTITE HOLES, AND HAMILTONIAN PROPERTIES.

A NOTE ON MINIMUM DEGREE, BIPARTITE HOLES, AND HAMILTONIAN PROPERTIES.

Authors :
QIANNAN ZHOU
BROERSMA, HAJO
LIGONG WANG
YONG LU
Source :
Discussiones Mathematicae: Graph Theory. 2024, Vol. 44 Issue 2, p717-726. 10p.
Publication Year :
2024

Abstract

We adopt the recently introduced concept of the bipartite-hole-number due to McDiarmid and Yolov, and extend their result on Hamiltonicity to other Hamiltonian properties of graphs with a large minimum degree in terms of this concept. An (s, t)-bipartite-hole in a graph G consists of two disjoint sets of vertices S and T with |S| = s and |T| = t such that E(S, T) = ∅. The bipartite-hole-numbere ᾶ(G) is the maximum integer r such that G contains an (s, t)-bipartite-hole for every pair of nonnegative integers s and t with s + t = r. Our main results are that a graph G is traceable if δ(G) ≥ e ᾶ(G) - 1, and Hamilton-connected if δ(G) ≥ e ᾶ(G) + 1, both improving the analogues of Dirac's Theorem for traceable and Hamilton-connected graphs. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
12343099
Volume :
44
Issue :
2
Database :
Academic Search Index
Journal :
Discussiones Mathematicae: Graph Theory
Publication Type :
Academic Journal
Accession number :
177835997
Full Text :
https://doi.org/10.7151/dmgt.2464