Maximization of distances of regular polygons on a circle

In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.

Polar graphs and railway traffic

Bohdan Zelinka (1974)

Aplikace matematiky

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On the existence of a cycle of length at least 7 in a (1,≤ 2)-twin-free graph

David Auger, Irène Charon, Olivier Hudry, Antoine Lobstein (2010)

Discussiones Mathematicae Graph Theory

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We consider a simple, undirected graph G. The ball of a subset Y of vertices in G is the set of vertices in G at distance at most one from a vertex in Y. Assuming that the balls of all subsets of at most two vertices in G are distinct, we prove that G admits a cycle with length at least 7.

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