# Recognizing weighted directed cartesian graph bundles

Discussiones Mathematicae Graph Theory (2000)

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

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topBlaz 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 -

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