New concept of connection in bidirected graphs
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 351-357.

In bidirected graph an edge has a direction at each end. We introduce a new definition of connection in a bidirected graph. We prove some properties of this definition and we establish a relationship to connection and imbalance in the corresponding signed graph. The main result gives a sufficient condition for a signed graph to have a Biconnected biorientation.

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Accepté le :
DOI : 10.1051/ro/2017053
Classification : 05C22, 05C38
Mots-clés : Matroid, signed graphs, bidirected graphs
Bessouf, Ouahiba 1 ; Khelladi, Abdelkader 1

1 
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     author = {Bessouf, Ouahiba and Khelladi, Abdelkader},
     title = {New concept of connection in bidirected graphs},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {351--357},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {2},
     year = {2018},
     doi = {10.1051/ro/2017053},
     zbl = {1398.05119},
     mrnumber = {3817469},
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Bessouf, Ouahiba; Khelladi, Abdelkader. New concept of connection in bidirected graphs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 351-357. doi : 10.1051/ro/2017053. http://www.numdam.org/articles/10.1051/ro/2017053/

[1] O. Bessouf, Théorème de Menger dans les graphes biorientés. Thèse de magister. U S. T H. B Faculté de Mathematiques (U.S.T.H.B) Alger, Mars (1999)

[2] F. Harary, On the notion of balance of a signed graph. Michigan Math. J. 2 (1953) 143–146 | DOI | MR | Zbl

[3] A. Khelladi, Propriétés algebriques de structures combinatoires. Thèse de doctorat d’état Institut de Mathématiques (U.S.T.H.B) Alger (1985)

[4] Thomas Zaslavsky, Signed graphs. Disc. Appl. Math. 4 (1982) 47–74 | DOI | MR | Zbl

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