A conjetura dos 3-fluxos de Tutte e emparelhamentos em grafos bipartidos

Orientador : Ricardo DahabDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoMestrad

Tutte's 3-flow conjecture and matchings in bipartite graphs

Tutte's 3-flow conjecture is equivalent to the assertion that there exists an orientation of the edges of a 4-edge-connected, 5-regular graph G for which the out-flow at each vertex is +3 or -3. The existence of one such orientation of the edges implies the existence of an equipartition of the vertices of G that separates the two possible types of vertices. Such an equipatition is called mod 3-orientable. We give necessary and sufficient conditions for the existence of mod 3-orientable equipartitions in general 5-regular graphs, in terms of (i) a perfect matching of a bipartite graph derived from the equipartition and (ii) the sizes of cuts in G. Also, we give a polynomial time algorithm for testing whether an equipartition of a 5-regular graph is mod 3-orientable.76839

Tutte's 3-flow Conjecture And Matchings In Bipartite Graphs

Tutte's 3-flow conjecture is restated as the problem of finding an orientation of the edges of a 4-edge-connected, 5-regular graph G, for which the out-flow at each vertex is +3 or -3. The induced equipartition of the vertices of G is called mod 3-orientable. We give necessary and sufficient conditions for the existence of mod 3-orientable equipartitions in general 5-regular graphs, in terms of (i) a perfect matching of a bipartite graph derived from the equipartition and (ii) the size of cuts in G.7114117Bondy, J.A., Murty, U.S.R., (1976) Graph Theory with Applications, , Elsevier North HollandDe Almeida E Silva, L.M., (1991) Fluxos Inteiros Em Grafos, , Master's thesis, UNICAMPYounger, D.H., Integer Flows (1983) J. Graph Theory, 7, pp. 349-357Zhang, C.-Q., (1997) Integer Flows and Cycle Covers of Graphs, , Marcel Dekke