Displaying similar documents to “Route systems and bipartite graphs”

Heavy subgraph pairs for traceability of block-chains

Binlong Li, Hajo Broersma, Shenggui Zhang (2014)

Discussiones Mathematicae Graph Theory

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A graph is called traceable if it contains a Hamilton path, i.e., a path containing all its vertices. Let G be a graph on n vertices. We say that an induced subgraph of G is o−1-heavy if it contains two nonadjacent vertices which satisfy an Ore-type degree condition for traceability, i.e., with degree sum at least n−1 in G. A block-chain is a graph whose block graph is a path, i.e., it is either a P1, P2, or a 2-connected graph, or a graph with at least one cut vertex and exactly two...

Route systems of a connected graph

Ladislav Nebeský (1994)

Mathematica Bohemica

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The concept of a route system was introduced by the present author in [3].Route systems of a connected graph G generalize the set of all shortest paths in G . In this paper some properties of route systems are studied.

The Path-Distance-Width of Hypercubes

Yota Otachi (2013)

Discussiones Mathematicae Graph Theory

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The path-distance-width of a connected graph G is the minimum integer w satisfying that there is a nonempty subset of S ⊆ V (G) such that the number of the vertices with distance i from S is at most w for any nonnegative integer i. In this note, we determine the path-distance-width of hypercubes.