Enumeration of hamiltonian paths in Caley diagrams.
David Housman (1981)
Aequationes mathematicae
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David Housman (1981)
Aequationes mathematicae
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W.T. Tutte (1977)
Aequationes mathematicae
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C.ST.J.A. NASH-WILLIAMS (1971)
Aequationes mathematicae
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Moshe Rosenfeld (1989)
Aequationes mathematicae
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Jianxiang Cao, Minyong Shi, Lihua Feng (2016)
Discussiones Mathematicae Graph Theory
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The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn with the same number of links and processors. For a bipartite graph G = (V0 ∪ V1,E), we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ Vi, i ∈ {0, 1}, any edge e ∈ E(G − v), there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn...
Branko Grünbaum, J. Malkevitch (1975)
Aequationes mathematicae
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Linda M. Lesniak (1978)
Aequationes mathematicae
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E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
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Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
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Tudor Zamfirescu (1971)
Rendiconti del Seminario Matematico della Università di Padova
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B.A. Kupershmidt, George Wilson (1980/81)
Inventiones mathematicae
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Jens-P. Bode, Anika Fricke, Arnfried Kemnitz (2015)
Discussiones Mathematicae Graph Theory
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In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+ 1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity...