Mutually Independent Hamiltonian Cycles of Cn x Cn
ثبت نشده
چکیده
منابع مشابه
Mutually Independent Hamiltonian Cycles
A Hamiltonian cycle of a graph G is a cycle which contains all vertices of G. Two Hamiltonian cycles C1 = 〈u0, u1, u2, ..., un−1, u0〉 and C2 = 〈v0, v1, v2, ..., vn−1, v0〉 in G are independent if u0 = v0, ui 6= vi for all 1 ≤ i ≤ n − 1. If any two Hamiltonian cycles of a Hamiltonian cycles set C = {C1, C2, ..., Ck} are independent, we call C is mutually independent. The mutually independent Hami...
متن کاملA New Property of Interconnection Networks
A graph G is pancyclic if G includes cycles of all lengths and G is edge-pancyclic if each edge lies on cycles of all lengths. A bipartite graph is edge-bipancyclic if each edge lies on cycles of every even length from 4 to |V (G)|. Two cycles with the same length m, C1 = ⟨u1, u2, · · · , um, u1⟩ and C2 = ⟨v1, v2, · · · , vm, v1⟩ passing through an edge (x, y) are independent with respect to th...
متن کاملProblems remaining NP-complette for sparse or dense graphs
For each fixed pair α, c > 0 let INDEPENDENT SET (m ≤ cn) and INDEPENDENT SET (m ≥ n2 ) − cn) be the problem INDEPENDENT SET restricted to graphs on n vertices with m ≤ cn or m ≥ n2 )− cn edges, respectively. Analogously, HAMILTONIAN CIRCUIT (m ≤ n + cn) and HAMILTONIAN PATH (m ≤ n + cn) are the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted to graphs with m ≤ n + cn edges. For ea...
متن کاملMutually Independent Hamiltonian Cycles of Pancake Networks
A hamiltonian cycle C of G is described as 〈u1, u2, . . . , un(G), u1〉 to emphasize the order of nodes in C. Thus, u1 is the beginning node and ui is the i-th node in C. Two hamiltonian cycles of G beginning at a node x, C1 = 〈u1, u2, . . . , un(G), u1〉 and C2 = 〈v1, v2, . . . , vn(G), v1〉, are independent if x = u1 = v1, and ui 6= vi for every 2 ≤ i ≤ n(G). A set of hamiltonian cycles {C1, C2,...
متن کاملMaximizing hamiltonian pairs and k-sets via numerous leaves in a tree
Sharp exponential upper bound, k!n−1, on the number of hamiltonian k-sets (i.e., decompositions into k hamiltonian cycles) among multigraphs G is found if the number, n, of vertices is fixed, n ≥ 3. Moreover, the upper bound is attained iff G = Cn where Cn is the k-fold n-cycle Cn. Furthermore, if G 6= Cn then the number of hamiltonian k-sets in G is less than or equal to k!n−1/k, the bound, if...
متن کامل