Geodesic
On imbalances in oriented bipartite graphs
Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 136-141 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An oriented bipartite graph is the result of assigning a direction to each edge of a simple bipartite graph. For any vertex $x$ in an oriented bipartite graph $D(U,V)$, let $d_{x}^{+}$ and $d_{x}^{-}$ respectively denote the outdegree and indegree of $x$. Define $a_{u_{i}}=d_{u_{i}}^{+}-d_{u_{i}}^{-}$ and $b_{v_{j}}=d_{v_{j}}^{+}-d_{v_{j}}^{-}$ respectively as the imbalances of vertices $u_i$ in $U$ and $v_j$ in $V$. In this paper, we obtain constructive and existence criteria for a pair of sequences of integers to be the imbalances of some oriented bipartite graph. We also show the existence of a bipartite oriented graph with given imbalance set. 
@article{EMJ_2010_1_2_a9,
     author = {U. Samee and T. A. Chishti},
     title = {On imbalances in oriented bipartite graphs},
     journal = {Eurasian mathematical journal},
     pages = {136--141},
     year = {2010},
     volume = {1},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a9/}
}
TY  - JOUR
AU  - U. Samee
AU  - T. A. Chishti
TI  - On imbalances in oriented bipartite graphs
JO  - Eurasian mathematical journal
PY  - 2010
SP  - 136
EP  - 141
VL  - 1
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a9/
LA  - en
ID  - EMJ_2010_1_2_a9
ER  - 
%0 Journal Article
%A U. Samee
%A T. A. Chishti
%T On imbalances in oriented bipartite graphs
%J Eurasian mathematical journal
%D 2010
%P 136-141
%V 1
%N 2
%U http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a9/
%G en
%F EMJ_2010_1_2_a9
U. Samee; T. A. Chishti. On imbalances in oriented bipartite graphs. Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 136-141. http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a9/

[1] D. Mubayi, T. G. Will, D. B. West, “Realizing degree imbalances in directed graphs”, Discrete Mathematics, 239 (2001), 147–153 | DOI | MR | Zbl

[2] S. Pirzada, Merajuddin, Yin Jainhua, “On the scores of oriented bipartite graphs”, J. Math. Study, 33:4 (2000), 354–359 | MR | Zbl

[3] S. Pirzada, “On imbalances in digraphs”, Kragujevac J. Mathematics, 31 (2008), 143–146 | MR | Zbl

[4] S. Pirzada, T. A. Naikoo, T. A. Chishti, “Score sets in oriented bipartite graphs”, Novi Sad J. Mathematics, 36:1 (2006), 35–45 | MR | Zbl