Let G be a 2-edge-connected graph with m edges and n vertices. The following two conjectures are proved in this paper. (i) The edges of G can be covered by circuits of total length at most m+n&1. (ii) The vertices of G can be covered by circuits of total length at most 2(n&1), where n 2. 1998 Acad
โฆ LIBER โฆ
Bijective proofs of two broken circuit theorems
โ Scribed by Andreas Blass; Bruce Eli Sagan
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 362 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
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In (J Graph Theory 33 (2000) , 14-24), Hell and Zhu proved that if a series-parallel graph G has girth at least 2 (3k -1) / 2 , then c (G) โค 4k / (2k -1). In (J Graph Theory 33 (2000), [185][186][187][188][189][190][191][192][193][194][195][196][197][198], Chien and Zhu proved that the girth condit