✦ LIBER ✦

Existence of spanning and dominating trails and circuits

✍ Scribed by H. J. Veldman

Publisher: John Wiley and Sons
Year: 1986
Tongue: English
Weight: 445 KB
Volume: 10
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190100105

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✦ Synopsis

Let T be a trail of a graph G. T is a spanning trail (S-trail) if T contains all vertices of G. Tis a dominating trail (D-trail) if every edge of G is incident with a t least one vertex of T. A circuit is a nontrivial closed trail.

Sufficient conditions involving lower bounds on the degree-sum of vertices or edges are derived for graphs to have an S-trail, S-circuit, D-trail, or D-circuit. Thereby a result of Brualdi and Shanny and one mentioned by Lesniak-Foster and Williamson are improved.

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