On randomly Hamiltonian graphs

On randomly -dimensional graphs

✍ Mohsen Jannesari; Behnaz Omoomi 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 254 KB

## a b s t r a c t For an ordered set W = {w 1 , w 2 , . . . , w k } of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W representation of v with respect to W , where d(x, y) is the distance between the vertices x and y. The set W is called a resolving set for G if disti

On hamiltonian line graphs

✍ Lane Clark 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 191 KB

On hamiltonian-connected graphs

✍ Ronald J. Gould; Xingxing Yu 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 735 KB

## Abstract One of the most fundamental results concerning paths in graphs is due to Ore: In a graph __G__, if deg __x__ + deg __y__ ≧ |__V__(__G__)| + 1 for all pairs of nonadjacent vertices __x, y__ ≅ __V__(__G__), then __G__ is hamiltonian‐connected. We generalize this result using set degrees.

On F-Hamiltonian graphs

✍ Zhenqi Yang 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 390 KB

Suppose G is a graph, F is a l-factor of G. G is called F-Hamiltonian, if there exists a Hamiltonian cycle containing F in G. In this paper, two necessary and sufficient conditions for a general graph and a bipartite graph being F-Hamiltonian are provided, respectively.

On critically hamiltonian graphs

✍ Linda Lesniak-Foster 📂 Article 📅 1977 🏛 Akadmiai Kiad 🌐 English ⚖ 216 KB

Randomly matchable graphs

✍ David P. Summer 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 190 KB

## Abstract A graph is defined to be randomly matchable if every matching of __G__ can be extended to a perfect matching. It is shown that the connected randomly matchable graphs are precisely __K__~2__n__~ and __K~n,n~__ (__n__ ≥ 1).