B. Alspach. Research problem 59. Discrete Mathematics, 50:115, 1984. Home/Search Document Not in Database Summary Related Articles Check |
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Hamilton circuits in directed Butterfly networks. - Bermond, Darrot, Delmas.. (1996) (1 citation) (Correct)
....distributed across the network. Various results have been obtained on the existence of Hamilton cycles in classical networks (see for example the survey [2, 11] For example it is well known that any Cayley graph on an abelian group is hamiltonian. Furthermore it has been conjectured by Alspach [1] that: Conjecture 1.8 (Alspach) Every connected Cayley graph on an abelian group has a Hamilton decomposition. This conjecture has been verified for all connected 4 regular graphs on abelian groups in [9] That includes in particular the toroidal meshes (grids) For the hypercube it is also ....
B. Alspach. Research problem 59. Discrete Mathematics, 50:115, 1984.
Hamilton cycle decomposition of the Butterfly network - Bermond, Darrot, Delmas.. (1996) (Correct)
.... WBF(3; 3) 1.2 Results Various results have been obtained on the existence of Hamilton cycles in classical networks (see for example the surveys [2, 7] For example, it is well known that any Cayley graph on an abelian group is hamiltonian. Furthermore, it has been conjectured by Alspach [1] that: Conjecture 1 (Alspach) Every connected Cayley graph on an abelian group has a Hamilton decomposition. This conjecture has been verified for all connected 4 regular graphs on abelian groups in [6] It includes in particular the toroidal meshes (grids) For the hypercube, it is also known ....
B. Alspach. Research problem 59. Discrete Mathematics, 50:115, 1984.
Hamilton circuits in the directed Butterfly network - Bermond, Darrot, Delmas.. (1996) (1 citation) (Correct)
....distributed across the network. Various results have been obtained on the existence of Hamilton cycles in classical networks (see for example the survey [2, 11] For example it is well known that any Cayley graph on an abelian group is hamiltonian. Furthermore it has been conjectured by Alspach [1] that: Conjecture 1 (Alspach) Every connected Cayley graph on an abelian group has a Hamilton decomposition. This conjecture has been verified for all connected 4 regular graphs on abelian groups in [9] That includes in particular the toroidal meshes (grids) For the hypercube it is also known ....
B. Alspach. Research problem 59. Discrete Mathematics, 50:115, 1984.
A Survey of Combinatorial Gray Codes - Savage (1996) (23 citations) (Correct)
....with the partial order, that is, if x i x j in the partial order, then i j. The problem of efficiently generating all the linear extensions of a poset, in any order, has been studied in [KV83, KS74, VR81] The area of Gray codes for linear extensions of a poset was introduced by Frank Ruskey in [Rus88b, PR91] as a setting in which to generalize the study of Gray codes for combinatorial objects. For example, if the Hasse diagram of the poset consists of two disjoint chains, one of length m and the other of length n, then there is a one to one correspondence between the linear extensions of the poset ....
....described in [Rus92] 25 To study the existence of Gray codes, Ruskey constructs a transposition graph corresponding to a given poset. The vertices are the linear extensions of the poset, two vertices being joined by an edge if they differ by a transposition. The resulting graph is bipartite. In [Rus88b], Ruskey makes the conjecture that whenever the parity difference is at most one, the graph of the poset has a Hamilton path. The conjecture is shown to be true for some special cases in [Rus92] including posets whose Hasse diagram consists of disjoint chains and for series parallel posets in ....
F. Ruskey. Research problem 90. Discrete Mathematics, 70:111--112, 1988.
Disjoint Hamiltonian cycles in recursive circulant graphs - Micheneau (1995) (1 citation) (Correct)
....vertex of G exactly one. A regular graph of degree n is said to have a Hamilton decomposition if its edge set can be partitioned into 1 2 n Hamilton cycles when n is even or into 1 2 (n Gamma 1) Hamilton cycles and a 1 factor when n is odd. This property is important in many applications. In [1], B. Alspach asked the following question: Is it the case that every connected Cayley graph X(G;H) on an abelian group G admits a Hamilton decomposition Some cases have been resolved [5] B. Alspach proved that Hamilton decomposability of vertex transitive Cayley graphs of order 2p, where p is ....
B. Alspach, Discrete Mathematics, problems, 50 (1984) 115.
Hamilton cycle decomposition of the Butterfly networks. - Bermond, Darrot, Delmas.. (1996) (Correct)
.... WBF(3; 3) 1.2 Results Various results have been obtained on the existence of Hamilton cycles in the classical networks (see for example the surveys [2, 7] For example it is well known that any Cayley graph on an abelian group is hamiltonian. Furthermore it has been conjectured by Alspach [1] that: Conjecture 1 (Alspach) Every connected Cayley graph on an abelian group has a Hamilton decomposition. This conjecture has been verified for all connected 4 regular graphs on abelian groups in [5] That includes in particular the toroidal meshes (grids) For the hypercube it is also known ....
B. Alspach. Research problem 59. Discrete Mathematics, 50:115, 1984.
Hamilton circuits in the directed wrapped Butterfly.. - Bermond, Darrot, Delmas, .. (1996) (Correct)
....across the network. Various results have been obtained about the existence of Hamilton cycles in classical networks (see for example the survey [2, 11] For example it is well known that any Cayley graph on an abelian group is Hamiltonian. Furthermore it has been conjectured by Alspach [1] that: Conjecture 1 (Alspach) Every connected Cayley graph on an abelian group has a Hamilton decomposition. This conjecture has been verified for all connected 4 regular graphs on abelian groups in [9] This includes in particular the toroidal meshes (grids) It is also known that H(2d) the ....
B. Alspach. Research problem 59. Discrete Mathematics, 50:115, 1984.
Hamilton circuits in the directed Butterfly network - Bermond, Darrot, Delmas.. (1996) (1 citation) (Correct)
....distributed across the network. Various results have been obtained on the existence of Hamilton cycles in classical networks (see for example the survey [2, 11] For example it is well known that any Cayley graph on an abelian group is Hamiltonian. Furthermore it has been conjectured by Alspach [1] that: Conjecture 1 (Alspach) Every connected Cayley graph on an abelian group has a Hamilton decomposition. This conjecture has been verified for all connected 4 regular graphs on abelian groups in [9] That includes in particular the toroidal meshes (grids) For the hypercube of dimension 2d ....
B. Alspach. Research problem 59. Discrete Mathematics, 50:115, 1984.
Hamilton cycle decomposition of the Butterfly network - Wo Rk (Correct)
.... WBF(3; 3) 1.2 Results Various results have been obtained on the existence of Hamilton cycles in classical networks (see for example the surveys [2, 7] For example, it is well known that any Cayley graph on an abelian group is hamiltonian. Furthermore, it has been conjectured by Alspach [1] that: Conjecture 1 (Alspach) Every connected Cayley graph on an abelian group has a Hamilton decomposition. This conjecture has been verified for all connected 4 regular graphs on abelian groups in [6] It includes in particular the toroidal meshes (grids) For the hypercube, it is also known ....
B. Alspach. Research problem 59. Discrete Mathematics, 50:115, 1984.
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