Antisymmetrical Digraphs
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1101-1117

Voir la notice de l'article provenant de la source Cambridge University Press

We call a digraph “antisymmetrical” if there is an automorphism θ of its graph, of period 2, which reverses the direction of every edge and maps no edge or vertex onto itself. We construct a theory of flows invariant under θ for such a diagraph. This theory is analogous to the Max Flow Min Cut theory for ordinary flows in digraphs. It is found to include that part of the theory of undirected graphs which discusses the existence of spanning subgraphs with a specified valency at each vertex.
Tutte, W. T. Antisymmetrical Digraphs. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1101-1117. doi: 10.4153/CJM-1967-101-8
@article{10_4153_CJM_1967_101_8,
     author = {Tutte, W. T.},
     title = {Antisymmetrical {Digraphs}},
     journal = {Canadian journal of mathematics},
     pages = {1101--1117},
     year = {1967},
     volume = {19},
     number = {1},
     doi = {10.4153/CJM-1967-101-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-101-8/}
}
TY  - JOUR
AU  - Tutte, W. T.
TI  - Antisymmetrical Digraphs
JO  - Canadian journal of mathematics
PY  - 1967
SP  - 1101
EP  - 1117
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-101-8/
DO  - 10.4153/CJM-1967-101-8
ID  - 10_4153_CJM_1967_101_8
ER  - 
%0 Journal Article
%A Tutte, W. T.
%T Antisymmetrical Digraphs
%J Canadian journal of mathematics
%D 1967
%P 1101-1117
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-101-8/
%R 10.4153/CJM-1967-101-8
%F 10_4153_CJM_1967_101_8

[1] 1. Belck, H. B., Reguläre Faktoren von Graphen, J. Reine Angew. Math., 188 (1950), 228–252. Google Scholar

[2] 2. Edmonds, J., Paths, trees and flowers, Can. J. Math., 17 (1965), 449–467. Google Scholar

[3] 3. Ford, L. R. Jr., and Fulkerson, D. R., Flows in networks (Princeton, 1962). Google Scholar

[4] 4. Gallai, T., On factorization of graphs, Acta Math. Acad. Sci. Hungar., 1 (1950), 133–153. Google Scholar

[5] 5. Gallai, T., Maximum-minimum Sätze una verallgemeinerte Faktoren von Graphen, Acta Math. Acad. Sci. Hungar., 12 (1961), 131–173. Google Scholar

[6] 6. Ore, O., Graphs and subgraphs, I-II, Trans. Amer. Math. Soc., 84 (1957), 109–136 and 93 (1959), 185-204. Google Scholar

[7] 7. Petersen, J., Die Theorie der regularen Graphs, Acta Math., 15 (1891), 193–220. Google Scholar

[8] 8. Sainte-Lagüe, A., Les réseaux, Mém. Sci. Math. (Paris), 18 (1926). Google Scholar

[9] 9. Tutte, W. T., The factorization of linear graphs, J. London Math. Soc., 22 (1947), 107–111. Google Scholar

[10] 10. Tutte, W. T., The factors of graphs, Can. J. Math., 4 (1952), 314–328. Google Scholar

Cité par Sources :