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A NOTE ON MINIMUM DEGREE, BIPARTITE HOLES, AND HAMILTONIAN PROPERTIES.
A NOTE ON MINIMUM DEGREE, BIPARTITE HOLES, AND HAMILTONIAN PROPERTIES.
- 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]
- Subjects :
- *BIPARTITE graphs
*HAMILTONIAN graph theory
Subjects
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