Measuring graph similarity is a key issue in many applications. We propose a new constraint-based modeling language for defining graph similarity measures by means of constraints. It covers measures based on univalent matchings, such that each node is matched with at most one node, as well as multivalent matchings, such that a node may be matched with a set of nodes. This language is designed o...

In this paper, vectors are column vectors. Unless otherwise specified, the norm of a matrix ‖M‖ is the Frobenius norm, defined by ‖M‖ = √∑ i,jM 2 ij . The all ones vector is denoted 1 and the all zeros vector is denoted 0. The all ones matrix is denoted J and the all zeros matrix is denoted O. The n× n identity matrix is denoted In, or simply I if its size is understood from context. The vector...

We describe an algorithm for graph matching which preserves global topological structure using an homology preserving graph matching. We show that for simplicial homology, graph matching is equivalent to finding an optimal simplicial chain map, which can be posed as a linear program satisfying boundary commutativity, simplex face intersection and assignment constraints. The homology preserving ...

In this paper we suggest an optimization approach to visual matching. We assume that the information available in an image may be conveniently represented symbolically in a relational graph. We concentrate on the problem of matching two such graphs. First we derive a cost function associated with graph matching and more precisely associated with relational subgraph isomorphism and with maximum ...

Graph data has been commonly used and widely researched both in academia and industry for many applications. And measuring similarity between graphs (i.e., graph matching) is the essential step for graph searching, pattern recognition and machine vision. At present, the most widely used approach to address the graph matching problem is graph edit distance (GED). However, the computation complex...

As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives few attention. In this paper, we first formalize the problem of simultaneously cutting a graph into two partitions i.e. graph cuts and establishing their cor...

A graph is called perfect matching compact (briefly, PM -compact), if its perfect matching graph is complete. Matching-covered PM -compact bipartite graphs have been characterized. In this paper, we show that any PM -compact bipartite graph G with δ(G) ≥ 2 has an ear decomposition such that each graph in the decomposition sequence is also PM -compact, which implies that G is matching-covered.

Kőnig-Egerváry graphs (KEGs) are the graphs whose maximum size of a matching is equal to the minimum size of a vertex cover. We give an excluded subgraph characterization of KEGs. We show that KEGs are a special case of a more general class of graph: Red/Blue-split graphs, and give an excluded subgraph characterization of Red/Blue-split graphs. We show several consequences of this result includ...

An r-edge-coloring of a graph is an assignment of r colors to the edges of the graph. An exactly r-edge-coloring of a graph is an r-edge-coloring of the graph that uses all r colors. A matching of an edge-colored graph is called rainbow matching, if no two edges have the same color in the matching. In this paper, we prove that an exactly r-edge-colored complete graph of order n has a rainbow ma...

The Hamiltonian cycle problem in digraph is mapped into a matching cover bipartite graph. Based on this mapping, it is proved that determining existence a Hamiltonian cycle in graph is O(n). Abstract. Hamiltonian Cycle, Z-mapping graph, complexity, decision, matching covered, optimization Hamiltonian Cycle, Z-mapping graph, complexity, decision, matching covered, optimization