A matching is indecomposable if it does not contain a nontrivial contiguous segment of vertices whose neighbors are entirely contained in the segment. We prove a Ramsey-like result for indecomposable matchings, showing that every sufficiently long indecomposable matching contains a long indecomposable matching of one of three types: interleavings, broken nestings, and proper pin sequences.

The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [3] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. For a recent survey, see Mühlherr [10...

In this paper the notion of stability of a bipartite matching is introduced and studied. It is a strong but overlooked constraint very useful in computational stereo. The resulting algorithms require no prior continuity model, are parameter-free, very fast, and accurate in terms of mismatches. A whole class of stable matchings is presented. It is shown that some of the popular matching algorith...

We prove a “General Manipulability Theorem” for general one-to-one two-sided matching markets with money. This theorem implies two folk theorems, the Manipulability Theorem and the General Impossibility Theorem, and provides a sort of converse of the Non-Manipulability Theorem (Demange, 1982, Leonard, 1983, Demange and Gale, 1985).

We present an extension of the ( )-calculus with a case construct that propagates through functions like a head linear substitution, and show that this construction permits to recover the expressiveness of ML-style pattern matching. We then prove that this system enjoys the Church-Rosser property using a semi-automatic `divide and conquer' technique by which we determine all the pairs of commut...

A retrospective fleet-sizing problem can be solved via bipartite matching, where a maximum cardinality matching corresponds to the minimum number of vehicles needed cover all trips. We prove min-max theorem on this fleet-size problem: pairwise incompatible trips is equal fleet size needed.

Matching is an extensively studied topic. The question we want to study here is the lower bound of a maximum matching in a graph. Earlier researchers studied the problem of the existence of a perfect matching (i.e. a matching of size n/2 with n vertices in a graph). Petersen [7] showed that a bridgeless cubic graph has a perfect matching. König [4] showed that there exists a perfect matching in...

In [18], Farrell and Whitehead investigate circulant graphs that are uniquely characterized by their matching and chromatic polynomials (i.e., graphs that are “matching unique” and “chromatic unique”). They develop a partial classification theorem, by finding all matching unique and chromatic unique circulants on n vertices, for each n ≤ 8. In this paper, we explore circulant graphs that are un...

We give a short proof of the following basic fact in matching theory: in a bipartite graph the maximum size of a matching equals the minimum size of a node cover. c © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 138–139, 2000

This paper studies the possibility of strategy-proof rules yielding satisfactory solutions to the matching problems. Alcalde and Barberá (1994) show that efficient and individually rational matching rules are manipulable in the one-to-one matching model. Thus, we pursue the possibility of strategy-proof matching rules by relaxing efficiency to a weaker condition of respect for unanimity. Our fi...