# Recognizing weighted directed cartesian graph bundles

• Volume: 20, Issue: 1, page 39-56
• ISSN: 2083-5892

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## Abstract

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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 ${}^{\to }\delta *$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.

## How to cite

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Blaz Zmazek, and Janez Zerovnik. "Recognizing weighted directed cartesian graph bundles." Discussiones Mathematicae Graph Theory 20.1 (2000): 39-56. <http://eudml.org/doc/270293>.

@article{BlazZmazek2000,
abstract = {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.},
author = {Blaz Zmazek, Janez Zerovnik},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph bundles; Cartesian graph product; weighted digraphs; half-convexity; recognizing Cartesian graph bundles},
language = {eng},
number = {1},
pages = {39-56},
title = {Recognizing weighted directed cartesian graph bundles},
url = {http://eudml.org/doc/270293},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Blaz Zmazek
AU - Janez Zerovnik
TI - Recognizing weighted directed cartesian graph bundles
JO - Discussiones Mathematicae Graph Theory
PY - 2000
VL - 20
IS - 1
SP - 39
EP - 56
AB - 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.
LA - eng
KW - graph bundles; Cartesian graph product; weighted digraphs; half-convexity; recognizing Cartesian graph bundles
UR - http://eudml.org/doc/270293
ER -

## References

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