Journal ArticleDOI
Connected, locally 2-connected, K1,3-free graphs are panconnected
S. V. Kanetkar,P. R. Rao +1 more
TLDR
It is proved that every connected, locally 2-connected graph containing no induced subgraph isomorphic to K1,3 is panconnected.Abstract:
A graph G is locally n-connected, n ≥ 1, if the subgraph induced by the neighborhood of each vertex is n-connected. We prove that every connected, locally 2-connected graph containing no induced subgraph isomorphic to K1,3 is panconnected.read more
Citations
More filters
Journal ArticleDOI
Claw-free graphs—a survey
TL;DR: This paper summarizes known results on claw-free graphs on n ⩽ 12 vertices and investigates the role of independence, domination, and other invariants in hamiltonicity.
Journal ArticleDOI
Updating the Hamiltonian problem—a survey
TL;DR: This article contains some material on related topics such as traceable, hamiltonian-connected and pancyclic graphs and digraphs, as well as an extensive bibliography of papers in the area.
Journal ArticleDOI
Hamiltonicity in claw-free graphs
TL;DR: In this article, the authors give a structural characterisation of claw-free graphs and give a polynomial algorithm for finding a Hamilton path (cycle) in a connected (2-connected) CN-free graph.
Journal ArticleDOI
Two-coloring random hypergraphs
TL;DR: In this paper, it was shown that if m = c 2kn then w.h.p H is not 2-colorable for c > ln 2/2.
Journal ArticleDOI
3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian
TL;DR: It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected and k-hamiltonian, which is a synonym for 1-triangular.
References
More filters
Journal ArticleDOI
A note on Hamiltonian circuits
Vašek Chvátal,Paul Erdös +1 more
TL;DR: G is s-connected and has no Hamiltonian circuit, but there are s paths starting at x and terminating in C which are pairwise disjoint apart from x and share with C just their terminal vertices.
Journal ArticleDOI
Every connected, locally connected nontrivial graph with no induced claw is hamiltonian
David J. Oberly,David P. Sumner +1 more
TL;DR: It is shown here that every connected, locally connected graph on p ≥ 3 vertices and having no induced K1,3 is Hamiltonian.
Journal ArticleDOI
A note on locally connected and hamiltonian-connected graphs
Gary Chartrand,Gary Chartrand,Ronald J. Gould,Ronald J. Gould,Albert D. Polimeni,Albert D. Polimeni +5 more
TL;DR: In this paper, it was shown that every connected, locally 3-connected graph containing no induced subgraph isomorphic to K(1, 3) is hamiltonian-connected.
Related Papers (5)
Every connected, locally connected nontrivial graph with no induced claw is hamiltonian
David J. Oberly,David P. Sumner +1 more