Displaying similar documents to “Graphs maximal with respect to absence of hamiltonian paths”

New sufficient conditions for hamiltonian and pancyclic graphs

Ingo Schiermeyer, Mariusz Woźniak (2007)

Discussiones Mathematicae Graph Theory

Similarity:

For a graph G of order n we consider the unique partition of its vertex set V(G) = A ∪ B with A = {v ∈ V(G): d(v) ≥ n/2} and B = {v ∈ V(G):d(v) < n/2}. Imposing conditions on the vertices of the set B we obtain new sufficient conditions for hamiltonian and pancyclic graphs.

On hyper-Zagreb index conditions for hamiltonicity of graphs

Yong Lu, Qiannan Zhou (2022)

Czechoslovak Mathematical Journal

Similarity:

During the last decade, several research groups have published results on sufficient conditions for the hamiltonicity of graphs by using some topological indices. We mainly study hyper-Zagreb index and some hamiltonian properties. We give some sufficient conditions for graphs to be traceable, hamiltonian or Hamilton-connected in terms of their hyper-Zagreb indices. In addition, we also use the hyper-Zagreb index of the complement of a graph to present a sufficient condition for it to...

A note on the Song-Zhang theorem for Hamiltonian graphs

Kewen Zhao, Ronald J. Gould (2010)

Colloquium Mathematicae

Similarity:

An independent set S of a graph G is said to be essential if S has a pair of vertices that are distance two apart in G. In 1994, Song and Zhang proved that if for each independent set S of cardinality k+1, one of the following condition holds: (i) there exist u ≠ v ∈ S such that d(u) + d(v) ≥ n or |N(u) ∩ N(v)| ≥ α (G); (ii) for any distinct u and v in S, |N(u) ∪ N(v)| ≥ n - max{d(x): x ∈ S}, then G is Hamiltonian. We prove that if for each...

On Uniquely Hamiltonian Claw-Free and Triangle-Free Graphs

Ben Seamone (2015)

Discussiones Mathematicae Graph Theory

Similarity:

A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. In this note, we prove that claw-free graphs with minimum degree at least 3 are not uniquely Hamiltonian. We also show that this is best possible by exhibiting uniquely Hamiltonian claw-free graphs with minimum degree 2 and arbitrary maximum degree. Finally, we show that a construction due to Entringer and Swart can be modified to construct triangle-free uniquely Hamiltonian graphs with minimum degree 3. ...

A conjecture on the prevalence of cubic bridge graphs

Jerzy A. Filar, Michael Haythorpe, Giang T. Nguyen (2010)

Discussiones Mathematicae Graph Theory

Similarity:

Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.