In this note we present answers to the open problems posed by Brualdi, Kiernan, Meyer and Schroeder in [Cyclic matching sequencibility of graphs, Australas. J. Combin. 53 (2012), 245–256]. 1 Discussion and response Let G ⊆ Kn be a graph of order n with m edges. The matching number of G is the maximum number of edges in a matching. The matching number of a linear ordering e1, e2, . . . , em of t...

We provide a new characterization of the NP-hard arc routing problem Rural Postman in terms of a constrained variant of minimum-weight perfect matching on bipartite graphs. To this end, we employ a parameterized equivalence between Rural Postman and Eulerian Extension, a natural arc addition problem in directed multigraphs. We indicate the NP-hardness of the introduced matching problem. In part...

Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of concept description languages (description logics), originally to help discard unimportant aspects of large concepts appearing in industrial-strength knowledge bases. This paper proposes a new approach to performing matching, based on a \concept-centered" normal form, ...

Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of concept description languages (description logics), originally to help discard unimportant aspects of large concepts appearing in industrial-strength knowledge bases. This paper proposes a new approach to performing matching, based on a \concept-centered" normal form, ...

The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted matching in a bipartite graph is equivalent to recognition a acyclic digraph. Based on these results, it proves that determine the bipartite graphs with all maxim...

We discuss the potentialities of structural matching as a compromise between fully-conceptual deep processing approaches and shallow bag-of-words approaches to answer seeking. We extended Collins's Tree Kernel [1] to formulate a new algorithm for soft structural matching, and we also developed and tested a method for combing structural matching with paraphrasing. Unfortunately, we found no posi...

A rainbow matching in an edge-colored graph is a matching in which all the edges have distinct colors. Wang asked if there is a function f(δ) such that a properly edgecolored graph G with minimum degree δ and order at least f(δ) must have a rainbow matching of size δ. We answer this question in the affirmative; an extremal approach yields that f(δ) = 98δ/23 < 4.27δ suffices. Furthermore, we giv...

The “stable marriage” problem is often described as follows. There are n men and n women; each of the men has an order of preference on the women, and each of the women has an order of preference on the men. A “matching” of the people into n man-woman pairs is said to be unstable if there exist some man and some woman who both prefer each other to their partner in the matching. If there is no s...

This year, we made changes to the passage/sentence retrieval component of ILQUA in handling factoid and list questions. All the other components remain same. ILQUA is an IE-driven QA system. To answer “Factoid” and “List” questions, we apply our answer extraction methods on NE-tagged passages or sentences. The answer extraction methods adopted here are surface text pattern matching, n-gram prox...

The decision making behaviors of humans and animals adapt and then satisfy an "operant matching law" in certain type of tasks. This was first pointed out by Herrnstein in his foraging experiments on pigeons. The matching law has been one landmark for elucidating the underlying processes of decision making and its learning in the brain. An interesting question is whether decisions are made deter...