Hamiltonian cycles in skirted trees
Hamiltonian Lines in Infinite Graphs with Few Verticles of Small Valency
Hamiltonian lines in the square of graphs. I. Hamiltonian circuits in the square of cacti
Hamiltonian lines in the square of graphs. II
Hamiltonian paths in the complete graph with edge-lengths 1, 2, 3.
Hamiltonian paths on Platonic graphs.
Hamiltonian shortage, path partitions of vertices, and matchings in a graph
Hamiltonian Simple Polytopes.
Hamiltonian virus-free digraphs.
Hamiltonian-colored powers of strong digraphs
For a strong oriented graph D of order n and diameter d and an integer k with 1 ≤ k ≤ d, the kth power of D is that digraph having vertex set V(D) with the property that (u, v) is an arc of if the directed distance from u to v in D is at most k. For every strong digraph D of order n ≥ 2 and every integer k ≥ ⌈n/2⌉, the digraph is Hamiltonian and the lower bound ⌈n/2⌉ is sharp. The digraph is distance-colored if each arc (u, v) of is assigned the color i where . The digraph is Hamiltonian-colored...
Hamiltonian-connected graphs and their strong closures.
Hamiltonicity and Generalised Total Colourings of Planar Graphs
The total generalised colourings considered in this paper are colourings of graphs such that the vertices and edges of the graph which receive the same colour induce subgraphs from two prescribed hereditary graph properties while incident elements receive different colours. The associated total chromatic number is the least number of colours with which this is possible. We study such colourings for sets of planar graphs and determine, in particular, upper bounds for these chromatic numbers for proper...
Hamiltonicity exponent of digraphs.
Hamiltonicity 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.
Hamiltonicity in Partly claw-free graphs
Matthews and Sumner have proved in [10] that if G is a 2-connected claw-free graph of order n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We say that a graph is almost claw-free if for every vertex v of G, 〈N(v)〉 is 2-dominated and the set A of centers of claws of G is an independent set. Broersma et al. [5] have proved that if G is a 2-connected almost claw-free graph of order n such that n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We generalize these results by considering the graphs...
Hamiltonicity 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 -presentation, that is, for groups generated by an involution and an element of order such that their product has order . More precisely, it is shown that the Cayley graph has a Hamilton cycle when (and thus ) is congruent to 2 modulo 4, and has a long cycle missing...
Hamiltonicity of -traceable graphs.
Hamiltonsche Linien im Quadrat brückenloser Graphen mit Artikulationen.
Hamiltonwege in rechteckigen und quaderförmigen Gittergraphen.
Harary Index of Product Graphs
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G × Km0,m1,...,mr−1 and the strong product G⊠Km0,m1,...,mr−1 , where Km0,m1,...,mr−1 is the complete multipartite graph with partite sets of sizes m0,m1, . . . ,mr−1 are obtained. Also upper bounds for the Harary indices of tensor and strong products of graphs are estabilished. Finally, the exact formula...