A graph G is quasi-brittle if every induced subgraph H of G contains a vertex which is incident to no edge extending symmetrically to a chordless path with three edges in either H or its complement 8. The quasi-britiie graphs turn out to be a natural generalization of the well-known class of brittle
โฆ LIBER โฆ
Perfectly orderable graphs are quasi-parity graphs: a short proof
โ Scribed by A. Hertz; D. de Werra
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 287 KB
- Volume
- 68
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
%'c shw that perfectly orderabk grapk Sa are q&-parity graphs by exhibiting two &lodes which are not llinked by a chordless odd chain. This proof is short and simpler than the one given by H. Meynid.
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A function between graphs is k-to-1 if each point in the codomain has precisely k pre-images in the domain. Given two graphs, G and H, and an integer k โฅ 1, and considering G and H as subsets of R 3 , there may or may not be a k-to-1 continuous function (i.e. a k-to-1 map in the usual topological se