A fractional matching of a graph G is a function f from E(G) to the interval [0, 1] such that ∑ e∈Γ(v) f(e) ≤ 1 for each v ∈ V (G), where Γ(v) is the set of edges incident to v. The fractional matching number of G, written α′∗(G), is the maximum of

The strong matching number sm( G) of a graph G is the maximum number of edges in G that induces a matching in the graph. For fixed o < p < 1, El Maftouhi and Marquez Gordones [Australasian Journal of Combinatorics 10 (1994), 97-104] showed that sm(Gn,p) is one of only a finite number of values for a.e. Gn,p E 9 (n, p). We show that, in fact, sm(Gn,p) is one of only two possible values for a.e. ...

The harmonic index of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, we determine the graph with minimum harmonic index among all unicyclic graphs with a perfect matching. Moreover, the graph with minimum harmonic index among all unicyclic graphs with a given matching num...

The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of minimum vertex covers (or independent sets), as well as the total number of vertex covers, and reduce the time complexity from O(n) to O(n log n), where n is the...

We determine the maximum number of edges that a claw-free graph can have, when its maximum degree and matching number are bounded. This is a famous problem that has been studied on general graphs, and for which there is a tight bound. The graphs achieving this bound contain in most cases an induced copy of K1,3, the claw, which motivates studying the question on claw-free graphs. Note that on g...

In matching with don’t-cares and k mismatches we are given a pattern of length m and a text of length n, both of which may contain don’t-cares (a symbol that matches all symbols), and the goal is to find all locations in the text that match the pattern with at most k mismatches, where k is a parameter. We present new algorithms that solve this problem using a combination of convolutions and a d...

More than forty years ago, Erdős conjectured that for any t ≤ nk , every k-uniform hypergraph on n vertices without t disjoint edges has at most max {( kt−1 k ) , ( n k ) − ( n−t+1 k )} edges. Although this appears to be a basic instance of the hypergraph Turán problem (with a t-edge matching as the excluded hypergraph), progress on this question has remained elusive. In this paper, we verify t...

To increase the computational efficiency of interestpoint based object retrieval, researchers have put remarkable research efforts into improving the efficiency of kNN-based feature matching, pursuing to match thousands of features against a database within fractions of a second. However, due to the highdimensional nature of image features that reduces the effectivity of index structures (curse...