منابع مشابه
Hamiltonicity of automatic graphs
It is shown that the existence of a Hamiltonian path in a planar automatic graph of bounded degree is complete for Σ1 1 , the first level of the analytical hierarchy. This sharpens a corresponding result of Hirst and Harel for highly recursive graphs. Furthermore, we also show: (i) The Hamiltonian path problem for finite planar graphs that are succinctly encoded by an automatic presentation is ...
متن کاملCollapsible Graphs and Hamiltonicity of Line Graphs
Thomassen conjectured that every 4-connected line graph is Hamiltonian. Chen and Lai (Combinatorics and Graph Theory, vol 95, World Scientific, Singapore, pp 53–69; Conjecture 8.6 of 1995) conjectured that every 3-edge connected and essentially 6-edge connected graph is collapsible. Denote D3(G) the set of vertices of degree 3 of graph G. For e = uv ∈ E(G), define d(e) = d(u)+ d(v)− 2 the edge ...
متن کاملHamiltonicity in multitriangular graphs
The family of 5–valent polyhedral graphs whose faces are all triangles or 3s–gons, s ≥ 9, is shown to contain non–hamiltonian graphs and to have a shortness exponent smaller than one.
متن کاملHamiltonicity of 3-Arc Graphs
An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a graph G is defined to have vertices the arcs of G such that two arcs uv, xy are adjacent if and only if (v, u, x, y) is a 3-arc of G. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-...
متن کاملHamiltonicity of cubic Cayley graphs
Following a problem posed by Lovász in 1969, it is believed that every finite connected vertex-transitive graph has a Hamilton path. This is shown here to be true for cubic Cayley graphs arising from finite groups having a (2, s, 3)-presentation, that is, for groups G = 〈a, b | a2 = 1, bs = 1, (ab)3 = 1, . . .〉 generated by an involution a and an element b of order s ≥ 3 such that their product...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90117-z