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Forbidden subgraphs of graphs uniquely Hamiltonian-connected from a vertex

โœ Scribed by George R.T. Hendry; C.J. Knickerbocker; Patti Frazer Lock; Michael Sheard

Book ID
108316194
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
356 KB
Volume
187
Category
Article
ISSN
0012-365X

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Graphs uniquely hamiltonian-connected fr
Graphs uniquely hamiltonian-connected from a vertex
โœ G.R.T Hendry ๐Ÿ“‚ Article ๐Ÿ“… 1984 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 558 KB

A graph G is called uniquely hamiitonian-connected from a vertex v if, for every vertex u ยข: v, there is exactly one v-u hamiltonian path in G. The main results are that if [ V(G)[ = n 3, then (1) deg(v) is even (2) n is odd, and ( ) IE(G)[<~(3n-3)I2. Several constructions of graphs uniquely hamilto

The size of graphs uniquely hamiltonian-
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โœ G.R.T Hendry ๐Ÿ“‚ Article ๐Ÿ“… 1986 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 220 KB

A graph G is called uniquely hamiltonian-connected from a vertex v of G if G contains exactly one v-u hamiltonian path for each vertex u, u ~ v. It is shown that if G is uniquely hamiltonian-connected from a vertex v and G has order n/> 5, then G has exactly ยฝ(3n-3) edges, G -v has exactly one hamil

Forbidden subgraphs and hamiitonian prop
Forbidden subgraphs and hamiitonian properties in the square of a connected graph
โœ Ronald J. Gould; Michael S. Jacobson ๐Ÿ“‚ Article ๐Ÿ“… 1984 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 331 KB ๐Ÿ‘ 1 views

Various Hamiltonian-like properties are investigated in the squares of connected graphs free of some set of forbidden subgraphs. The star K,+ the subdivision graph of &, and the subdivision graph of K1,3 minus an endvertex play central roles. In particular, we show that connected graphs free of the