Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Recognizing weighted directed cartesian graph bundles

100%

Zmazek B., Zerovnik J.

Discussiones Mathematicae Graph Theory

2000

tom 20

nr 1

39-56

In this paper we show that methods for recognizing Cartesian graph bundles can be generalized to weighted digraphs. The main result is an algorithm which lists the sets of degenerate arcs for all representations of digraph as a weighted directed Cartesian graph bundle over simple base digraphs not containing transitive tournament on three vertices. Two main notions are used. The first one is the new relation $^→δ*$defined among the arcs of a digraph as a weighted directed analogue of the well-known relation δ*. The second one is the concept of half-convex subgraphs. A subgraph H is half-convex in G if any vertex x ∈ G∖H has at most one predecessor and at most one successor.

Weak k-reconstruction of Cartesian products

81%

Imrich W., Zmazek B., Zerovnik J.

Discussiones Mathematicae Graph Theory

2003

tom 23

nr 2

273-285

By Ulam's conjecture every finite graph G can be reconstructed from its deck of vertex deleted subgraphs. The conjecture is still open, but many special cases have been settled. In particular, one can reconstruct Cartesian products. We consider the case of k-vertex deleted subgraphs of Cartesian products, and prove that one can decide whether a graph H is a k-vertex deleted subgraph of a Cartesian product G with at least k+1 prime factors on at least k+1 vertices each, and that H uniquely determines G. This extends previous work of the authors and Sims. The paper also contains a counterexample to a conjecture of MacAvaney.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Zerovnik J.

2 Zmazek B.

1 Imrich W.

1 2003

1 2000

Wyniki wyszukiwania

Recognizing weighted directed cartesian graph bundles

Weak k-reconstruction of Cartesian products