In this paper we show that properly edge-colored graphs Gwith |V (G)| ≥ 4δ(G) − 3 have rainbow matchings of size δ(G); this gives the best known bound for a recent question of Wang. We also show that properly edge-colored graphs Gwith |V (G)| ≥ 2δ(G) have rainbow matchings of size at least δ(G) − 2δ(G)2/3. This result extends (with a weaker error term) the well-known result that a factorization...

The stability number (G) of a graph G is the cardinality of a stability system of G (that is of a stable set of maximum size). A graph is -stable if its stability number remains the same upon both the deletion and the addition of any edge. Trying to generalize some stable trees properties, we show that there does not exist any -stable chordal graph, and we prove that: if G is a connected bipart...

A matching of size 2n is a partition of the set [2n] = {1, 2, . . . , 2n} into n disjoint pairs. A matching may be identified with a canonical sequence, which is a sequence of integers in which each integer i ∈ [n] occurs exactly twice, and the first occurrence of i precedes the first occurrence of i+ 1. A partial pattern with k symbols is a sequence of integers from the set [k], in which each ...

The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a degree-constrained subgraph instance, can we transform one solution into the other by adding and removing individual edges, such that each intermediate subgraph s...

In this paper, we determine the tight upper bound for the number of matchings of connected n-vertex tricyclic graphs. We show that this bound is 13fn−4+16fn−5, where fn be the nth Fibonacci number. We also characterize the n-vertex simple connected tricyclic graph for which the bound is best possible.

This paper deals with recognizing human actions in still images. We make two key contributions. (1) We propose a novel, 2.5D representation of action images that considers both view-independent pose information and rich appearance information. A 2.5D graph of an action image consists of a set of nodes that are key-points of the human body, as well as a set of edges that are spatial relationship...

This paper studies the falsifiability of two-sided matching theory when agents’ preferences are unknown. A collection of matchings is rationalizable if there are preferences for the agents involved so that the matchings are stable. We show that there are nonrationalizable collections of matchings; hence, the theory is falsifiable. We also characterize the rationalizable collections of matchings...

This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to one-shot deviation.

Let G be a connected bipartite graph. An involution α of G that preserves the bipartition of G is called bipartite. Let Gα be the graph obtained from G by adding to G the natural perfect matching induced by α. We show that the k-cube Qk is isomorphic to the direct product G×H if and only if G is isomorphic to Qk−1 for some bipartite involution α of Qk−1 and H = K2.