The Hungarian method is an e cient algorithm for nding a minimal cost perfect matching in a weighted bipartite graph. This paper describes an e cient algorithm for nding all minimal cost perfect matchings. The computational time required to generate each additional perfect matching is O(n(n + m)); and it requires O(n+m) memory storage. This problem can be solved by algorithms for nding the Kth-...

‎An  oriented perfect path double cover (OPPDC) of a‎ ‎graph $G$ is a collection of directed paths in the symmetric‎ ‎orientation $G_s$ of‎ ‎$G$ such that‎ ‎each arc‎ ‎of $G_s$ lies in exactly one of the paths and each‎ ‎vertex of $G$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete‎ ‎Math‎. ‎276 (2004) 287-294) conjectured that ...

Weakly labeled data are inevitable in various research areas artificial intelligence (AI) where one has a modicum of knowledge about the complete dataset. One reasons for weakly AI is insufficient accurately data. Strict privacy control or accidental loss may also cause missing-data problems. However, supervised machine learning (ML) requires order to successfully solve problem. Data labeling d...

A weakly-connected dominating set, W, of a graph, G, is a dominating set such that the subgraph consisting of V (G) and all edges incident with vertices in W is connected. Finding a small weaklyconnected dominating set of a graph has important applications in clustering mobile ad-hoc networks. In this paper we introduce several new randomised greedy algorithms for finding small weakly-connected...

Computing the circular chromatic number of a given planar graph is NP-complete, as it is already NP-complete to compute its chromatic number. In this note, we prove that the circular clique number of a planar graph, and therefore the circular chromatic number of a circular perfect graph, is computable in O(ne) time; outerplanar graphs are circular perfect.

Let H be any graph. We determine (up to an additive constant) the minimum degree of a graph G which ensures that G has a perfect H-packing. More precisely, let δ(H, n) denote the smallest integer k such that every graph G whose order n is divisible by |H| and with δ(G) ≥ k contains a perfect H-packing. We show that