Open Journal of Discrete Applied Mathematics
Vol. 6 (2023), Issue 3, pp. 26 – 29
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2023.0090
A note on the characterization of claw-free and paw-free graphs
Phillip Mafuta\(^{1,3,*}\), Josiah Mushanyu\(^{2,3}\)
\(^{1}\)Department of Mathematics and Applied Mathematics IB74, University of the Free State, Bloemfontein, South Africa; phillipmafuta@gmail.com
\(^{2}\)Department of Computing, Mathematical and Statistical Sciences, University of Namibia, Windhoek, Namibia; mushanyuj@gmail.com
\(^{3}\) Department of Mathematics and Computational Sciences, University of Zimbabwe, Harare, Zimbabwe
Copyright © 2023 Rikio Ichishima and Francesc-Antoni Muntaner-Batle. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: November 12, 2023 – Accepted: December 14, 2023 – Published: December 26, 2023
Abstract
A number of results on claw-free, paw-free graphs have been presented in the literature. Although the proofs of such results are elegant, sound and valid, it has gone unnoticed that all the results about claw-free, paw-free graphs in the literature are a consequence of a result by Olariu [1]. The note, apart from covering the aforementioned gap, also provides an alternate proof to a result by Faudree and Gould found in [2] in that, an unnoticed consequence resulted in the characterization of claw-free, paw-free graphs.
Keywords:
Forbidden Sub-graphs; Pancyclicity; Hamiltonicity; Traceability.