On -path hamiltonian graphs and line-graphs
Tudor Zamfirescu (1971)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
Tudor Zamfirescu (1971)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
Similarity:
E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
Similarity:
Jens-P. Bode, Anika Fricke, Arnfried Kemnitz (2015)
Discussiones Mathematicae Graph Theory
Similarity:
In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+ 1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity...
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...
Demovič, A. (1995)
Acta Mathematica Universitatis Comenianae. New Series
Similarity:
Gary Chartrand, S. F. Kapoor (1974)
Colloquium Mathematicae
Similarity:
Ordaz, Oscar, González, Leida, Márquez, Isabel, Quiroz, Domingo (2000)
Divulgaciones Matemáticas
Similarity:
Jill R. Faudree, Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson, Colton Magnant (2010)
Discussiones Mathematicae Graph Theory
Similarity:
The Chvátal-Erdös theorems imply that if G is a graph of order n ≥ 3 with κ(G) ≥ α(G), then G is hamiltonian, and if κ(G) > α(G), then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number condition in the presence of sufficient connectivity. More specifically, it is noted that if G is a graph of order n and k ≥ 2 is a positive integer such that κ(G) ≥ k, δ(G) >...
Ján Ninčák (1974)
Commentationes Mathematicae Universitatis Carolinae
Similarity: