Circuits containing specified edges

Title Number of Hamiltonian Circuits Containing Specified Edges in an Incom plete Graph and Its Application

A procedure for finding the number of Hamiltonian cir'cuits containing specined edges in a given incomplete graph is introduced and it is shown that the number of such Hamiltonian circuits can be expressed by a general fbrmula when the specified edges make a systematic form with all edges belonging to complement of the given incomplete graph. This procedure is applied to rnultigraphs with paral...

Vertex-disjoint cycles containing specified edges in a bipartite graph

Dirac and Ore-type degree conditions are given for a bipartite graph to contain vertex disjoint cycles each of which contains a previously specified edge. This solves a conjecture of Wang in [6].

Checking Equivalence for Circuits Containing Incompletely Specified Boxes

We consider the problem of checking whether an implementation which contains parts with incomplete information is equivalent to a given full specification. We study implementations which are not completely specified, but contain boxes which are associated with incompletely specified functions (called Incompletely Specified Boxes or IS– Boxes). After motivating the use of implementations with In...

Long cycles through specified edges and vertices

Eulerian subgraphs containing given edges

For an integer l¿0, de ne SE(l) to be the family of graphs such that G ∈SE(l) if and only if for any edge subset X ⊆E(G) with |X |6l, G has a spanning eulerian subgraph H with X ⊆E(H). The graphs in SE(0) are known as supereulerian graphs. Let f(l) be the minimum value of k such that every k-edge-connected graph is in SE(l). Jaeger and Catlin independently proved f(0) = 4. We shall determine f(...