DMCA
On Fans in Multigraphs (2005)
Cached
Download Links
- [www.math.sinica.edu.tw]
- [www.math.sinica.edu.tw]
- [www.math.sinica.edu.tw]
- DBLP
Other Repositories/Bibliography
| Venue: | JOURNAL OF GRAPH THEORY |
| Citations: | 7 - 5 self |
BibTeX
@ARTICLE{Cariolaro05onfans,
author = {David Cariolaro},
title = {On Fans in Multigraphs},
journal = {JOURNAL OF GRAPH THEORY},
year = {2005},
volume = {51},
pages = {301--318}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We introduce a unifying framework for studying edge-colouring problems on multigraphs. This is defined in terms of a rooted directed multigraph F which is naturally associated to the set of fans based at a given vertex u in a multigraph G. We call F the “Fan Digraph”. We show that fans in G based at u are in one-to-one correspondence with directed trails in F starting at the root of F. We state and prove a central theorem about the fan digraph, which embodies many edge-colouring results and expresses them at a higher level of abstraction. Using this result, we derive short proofs of classical theorems. We conclude with a new, generalized version of Vizing’s Adjacency Lemma for multigraphs, which is stronger than all those known to the author.
