Mathematics Subject Classification: 05C07, 05C12, 05C45, 05C69.
[29]Ver contenido en pdf.
Artículos
Ciclos hamiltonianos que pasan a través de un bosque lineal en grafos bipartitos balanceados
Hamiltonian cycles that pass through a linear forest of balanced bipartite graphs
1Departamento de Matemáticas, Universidad de Oriente, Cumaná, Venezuela. E-Mail: danieljosb@gmail.com, lmata73@gmail.com
2Departamento de Higiene y Seguridad Laboral, Universidad Politécnica Clodosbaldo Russián, Cumaná, Venezuela. E-Mail: hlramirez6@hotmail.com
Sea G = (A ∪ B,E) un grafo bipartito con |A| = |B| = n ≥ 4.
[17]Un grafo es un bosque lineal si cada componente es un camino. Sea S un conjunto de m lados de G que induce un bosque lineal. Probaremos que si σ 1,1 (G) = min{d G (u) + d G (v) : u ∈ A,v ∈ B,uv ̸∈ E(G)} ≥ (n+1)+m, entonces G contiene (m+1) ciclos hamiltonianos C j tal que |E(C j ) ∩ S| = j, con j = 0,1,...,m.
Palabras clave: grafo bipartito; bosque lineal; ciclo hamiltoniano
Let G = (A ∪ B,E) be a bipartite graph whith |A| = |B| = n ≥ 4.
[22]A graph is linear forest if every component is a path. Let S be a set of m edges of G that induces a linear forest. We prove that if σ 1,1 (G) = min{d G (u) + d G (v) : u ∈ A,v ∈ B,uv ̸∈ E(G)} ≥ (n + 1) + m, then G contains (m + 1) hamiltonian cycles C j such that |E(C j ) ∩ S| = j, with j = 0,1,...,m.
Keywords: bipartite graph; linear forest; hamiltonian cycle
Mathematics Subject Classification: 05C07, 05C12, 05C45, 05C69.
[29]Ver contenido en pdf.
Referencias
Chen, G.; Enomoto, H.; Lou, D.; Saito, A. (2001) “Vertex-disjoint cycles containing specified edges in a bipartite graph”, Australasian Journal of Combinatorics 23(1): 37-48. [ Links ]
Diestel, R. (2000) Graph Theory. Springer-Verlag, New York. [ Links ]
Posa, L. (1963) “On the circuits of finite graphs (russian summary)”, Magyar Tud. Akad. Mat. Kutató Int. Köz 8(1): 355-361. [ Links ]
Sugiyama, T. (2004) “Hamiltonian cycles through a linear forest”, SUT Journal of Mathematics 40(2): 103-109. [ Links ]
Wang, H. (1999) “Covering a bipartite graph with cycles passing through given edges”, Australasian Journal of Combinatorics 19(1): 115-121. [ Links ]
Recibido: 02 de Febrero de 2018; Revisado: 05 de Junio de 2018; Aprobado: 07 de Junio de 2018