WebAug 24, 2024 · Our main result states that graphs that have a robust Hamilton framework are (in a strong sense) Hamiltonian. As an application we can easily recover many of the above mentioned contributions and also prove several new results. 2 Results To provide an overview of our outcomes, we introduce some further notation. WebDaniel P. Biebighauser and M. N. Ellingham, Prism-hamiltonicity of triangulations, J. Graph Theory 57 (2008) 181-197. doi:10.1002/jgt.20276 , PDF preprint . M. N. Ellingham and D. Christopher Stephens, The nonorientable genus of joins of complete graphs with large edgeless graphs, J. Combinatorial Theory Series B 97 (2007) 827-845.
(PDF) Hamiltonicity in Prime Sum Graphs - ResearchGate
WebNov 1, 2013 · We also characterize connected k -regular graphs on 2 k + 3 vertices ( 2 k … WebMar 2, 2024 · A graph is Hamiltonian if it contains a cycle which visits every vertex of the … provincetown car rental companies
Hamiltonicity in connected regular graphs - ScienceDirect
Webgraph is connected if its underlying undirected graph is connected. That is, the connectedness of a directed graph does not depend on the orientation of directed edges. De nition 2.3 (Graph Isomorphism). For any graphs and 0, we de ne an isomorphism ˚: ! 0as a map between vertices in and vertices in 0such that, for v 1 and v 2 in fvg, if v 1 ... WebOct 27, 2024 · It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and, excluding the bipartite case, contains an odd cycle. Our main result in turn states that any large enough graph that robustly satisfies these properties must already be Hamiltonian. WebMay 19, 2016 · In the study of hamiltonicity of graphs, a classical result was proved by Chvátal and Erdös [ 10 ]. Theorem 1.2 (Chvátal and Erdös [ 10 ]) A connected graph G with \alpha (G)\le \kappa (G) is Hamiltonian. For claw-free graphs, Flandrin and Li [ 12] proved the following: Theorem 1.3 provincetown carnival week 2022