Gallai and Milgram (1960) proved that a digraph with stability number ct is spanned by ct disjoint directed paths. Chen and Manalastas Jr (1983) proved that a strong digraph with stability number at most two is spanned by at most two consistent directed circuits. We slightly simplify the proof of
A short proof of the two-commodity flow theorem
β Scribed by P.D Seymour
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 80 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Proof, There are d arithmdztic sequence8 inserted (mod 1) into [O, I], In the following, we will refer to the 'Mart" and "flni~h" points of each of the sequences, These are, respectively, the points {q) and {(q -I)@ t cu,) for 1 G i G d. The idea of the proof is to associate each interval in [O, I]
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) β€ 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