The Hamilton spaces of Cayley graphs on abelian groups
Discrete Mathematics
Hamiltonian paths and Hamiltonian connectivity in graphs
Discrete Mathematics
Basic graph theory: paths and circuits
Handbook of combinatorics (vol. 1)
On the square of a Hamiltonian cycle in dense graphs
Proceedings of the seventh international conference on Random structures and algorithms
The cycle space of a 3-connected Hamiltonian graph
Discrete Mathematics
Hamilton-connected Cayley graphs on Hamiltonian groups
European Journal of Combinatorics
2-factors in dense bipartite graphs
Discrete Mathematics - Kleitman and combinatorics: a celebration
How many random edges make a dense graph Hamiltonian?
Random Structures & Algorithms
On the number of Hamiltonian cycles in Dirac graphs
Discrete Mathematics
Combinatorica
The Cycle Space of an Infinite Graph
Combinatorics, Probability and Computing
Hamilton Cycles in Planar Locally Finite Graphs
SIAM Journal on Discrete Mathematics
Hamiltonian cycles in Dirac graphs
Combinatorica
Bandwidth, expansion, treewidth, separators and universality for bounded-degree graphs
European Journal of Combinatorics
The homology of a locally finite graph with ends
Combinatorica
Embedding spanning subgraphs into large dense graphs
Embedding spanning subgraphs into large dense graphs
Pósa's conjecture for graphs of order at least 2 × 108
Random Structures & Algorithms
Embedding into Bipartite Graphs
SIAM Journal on Discrete Mathematics
Approximate Hamilton decompositions of random graphs
Random Structures & Algorithms
Edge-disjoint Hamilton cycles in graphs
Journal of Combinatorial Theory Series B
Communication: House of Graphs: A database of interesting graphs
Discrete Applied Mathematics
Dirac's theorem for random graphs
Random Structures & Algorithms
Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups
Journal of Graph Theory
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For a graph G, let |G| denote its number of vertices, @d(G) its minimum degree and Z"1(G;F"2) its cycle space. Call a graph Hamilton-generated if and only if every cycle in G is a symmetric difference of some Hamilton circuits of G. The main purpose of this paper is to prove: for every @c0 there exists n"0@?Z such that for every graph G with |G|=n"0 vertices, (1)if @d(G)=(12+@c)|G| and |G| is odd, then G is Hamilton-generated, (2)if @d(G)=(12+@c)|G| and |G| is even, then the set of all Hamilton circuits of G generates a codimension-one subspace of Z"1(G;F"2) and the set of all circuits of G having length either |G|-1 or |G| generates all of Z"1(G;F"2), (3)if @d(G)=(14+@c)|G| and G is balanced bipartite, then G is Hamilton-generated. All these degree-conditions are essentially best-possible. The implications in (1) and (2) give an asymptotic affirmative answer to a special case of an open conjecture which according to [I.B.-A. Hartman, Long cycles generate the cycle space of a graph, European J. Combin. 4 (3) (1983) 237-246] originates with A. Bondy.