Edge-colorability of graph bundles

Pisanski, Tomazˇ; Shawe‐Taylor, John; Vrabec, Jozˇe

doi:10.1016/0095-8956(83)90076-x

Cited by 43 publications

(19 citation statements)

References 6 publications

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“…It is clear that for any G and permutation π , the generalized Cartesian product G P n is a fasciagraph. In 1983, Pisanski, Shawe-Taylor and Vrabec [10] introduced the notion of a graph bundle in a graph theoretic manner. to Aut(G), then this graph is a Cartesian graph bundle.…”

Section: Definitions and Backgroundmentioning

confidence: 99%

Domination of generalized Cartesian products

Benecke¹,

Mynhardt²

2010

Discrete Mathematics

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Section: Definitions and Backgroundmentioning

confidence: 99%

Domination of generalized Cartesian products

Benecke¹,

Mynhardt²

2010

Discrete Mathematics

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“…Here we assume that the bundle representation is given. (Graph bundles were first studied in [10].) Definition 2.4.…”

Section: Preliminariesmentioning

confidence: 99%

Fault-diameter of Cartesian graph bundles

Banič

Žerovnik

2006

Information Processing Letters

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“…We refer the reader to [13,40] and the references therein. The theory was extended to combinatorial graph bundles introduced by Pisanski and Vrabec [31] in the 1980s.…”

Section: Historymentioning

confidence: 99%

Lifting Graph Automorphisms by Voltage Assignments

Malnič

Nedela

Škoviera

2000

European Journal of Combinatorics

153

145

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The problem of lifting graph automorphisms along covering projections and the analysis of lifted groups is considered in a purely combinatorial setting. The main tools employed are: (1) a systematic use of the fundamental groupoid; (2) unification of ordinary, relative and permutation voltage constructions into the concept of a voltage space; (3) various kinds of invariance of voltage spaces relative to automorphism groups; and (4) investigation of geometry of the lifted actions by means of transversals over a localization set. Some applications of these results to regular maps on surfaces are given. Because of certain natural applications and greater generality, graphs are allowed to have semiedges. This requires careful re-examination of the whole subject and at the same time leads to simplification and generalization of several known results.

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Edge-colorability of graph bundles

Cited by 43 publications

References 6 publications

Domination of generalized Cartesian products

Domination of generalized Cartesian products

Fault-diameter of Cartesian graph bundles

Lifting Graph Automorphisms by Voltage Assignments

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