Recognizing weighted directed Cartesian graph bundles

Blaž Zmazek (Author), Janez Žerovnik (Author)

Abstract

Predstavljena je posplošitev prepoznavanja kartezičnih grafovskih svežnjev za utežene usmerjene grafe. Osrednji rezultat predstavlja algoritem, ki vrne množice degeneriranih vektorjev vseh predstavitev usmerjenih grafov v obliki uteženih usmerjenih kartezičnih grafovskih svežnjev nad baznimi grafi brez tranzitivnih turnirjev na treh točkah. Temeljna pojma pri izpeljavi tega rezutata sta relacija ▫$\vec{\delta}^\ast$▫ in polkonveksnost. Relacija ▫$\vec{\delta}^\ast$▫, definirana na množici vektorjev usmerjenega grafa, predstavlja posplošitev znane relacije ▫$\delta^\ast$▫. Podgraf ▫$H$▫ je polkonveksen v ▫$G$▫, če ima poljubna točka ▫$x \in G \setminus H$▫ največ enega predhodnika in največ enega naslednika.

Keywords

matematika;teorija grafov;grafovski svežnji;kartezični produkt grafov;uteženi digrafi;polkonveksnost;ne zaključna dela;mathematics;graph theory;graph bundles;Cartesian graph product;weighted digraphs;half-convexity;

Data

Language:	English
Year of publishing:	2000
Typology:	1.01 - Original Scientific Article
Organization:	UM FS - Faculty of Mechanical Engineering
UDC:	519.17
COBISS:	10205960
ISSN:	1234-3099
Views:	1303
Downloads:	379
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Prepoznavanje uteženih usmerjenih kartezičnih grafovskih svežnjev
Secondary 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 ▫$\vec{\delta}^\ast$▫ defined among the arcs of a digraph as a weighted directed analogue of the well-known relation ▫$\delta^\ast$▫. The second one is the concept of half-convex subgraphs. A subgraph ▫$H$▫ is half-convex in ▫$G$▫ if any vertex ▫$x \in G \setminus H$▫ has at most one predecessor and at most one successor
Secondary keywords:	Teorija grafov;
URN:	URN:SI:UM:
Type (COBISS):	Scientific work
Pages:	str. 39-56
Volume:	ǂVol. ǂ20
Issue:	ǂno. ǂ1
Chronology:	2000
ID:	9595947