Abstract

BRITO, Daniel; MARIN, Lope  and  RAMIREZ, Henry. Hamiltonian cycles that pass through a linear forest of balanced bipartite graphs. Rev. Mat [online]. 2018, vol.25, n.2, pp.347-365. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v25i2.33908.

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Let G = (A ∪ B,E) be a bipartite graph whith |A| = |B| = n ≥ 4.

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.

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