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Linear forests and ordered cycles

Guantao Chen; Ralph J. Faudree; Ronald J. Gould; Michael S. Jacobson; Linda Lesniak; Florian Pfender — 2004

Discussiones Mathematicae Graph Theory

A collection $L = P ¹ \cup P ² \cup . . . \cup P^{t}$ (1 ≤ t ≤ k) of t disjoint paths, s of them being singletons with |V(L)| = k is called a (k,t,s)-linear forest. A graph G is (k,t,s)-ordered if for every (k,t,s)-linear forest L in G there exists a cycle C in G that contains the paths of L in the designated order as subpaths. If the cycle is also a hamiltonian cycle, then G is said to be (k,t,s)-ordered hamiltonian. We give sharp sum of degree conditions for nonadjacent vertices that imply a graph is (k,t,s)-ordered hamiltonian.

On $k$ -ordered bipartite graphs.

Faudree, Jill R.; Gould, Ronald J.; Pfender, Florian; Wolf, Allison — 2003

The Electronic Journal of Combinatorics [electronic only]

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Linear forests and ordered cycles

On k -ordered bipartite graphs.

On $k$ -ordered bipartite graphs.