We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a perfect matching or not and (2) a unique perfect matching or not, are in the logspace complexity class SPL. Since SPL is contained in the logspace counting classe...

A t-spanner of a graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times their distance in G. Spanners arise in the context of approximating the original graph with a sparse subgraph (Peleg, D., and Scha ffer, A. A. (1989), J. Graph. Theory 13 (1), 99 116). The MINIMUM t-SPANNER problem seeks to find a t-spanner with the minimum number of edges f...

We construct moduli spaces of representations quivers over arbitrary schemes and show how pointed curves genus zero like the Grothendieck–Knudsen M ¯ 0,n Losev–Manin L n can be interpreted as inverse limits certain bipartite quivers. also investigate case more general Hassett 0,a weighted stable zero.

Several graph problems (e.g., steiner tree, connected domination, hamiltonian path, and isomorphismproblem), which can be solved in polynomialtime for distance-hereditary graphs, are NP-complete or open for parity graphs. Moreover, the metric characterizations of these two graph classes suggest an excessive gap between them. We introduce a family of classes forming an innnite lattice with respe...

Let L(Qt) denote the number of linear extensions of the t-dimensional Boolean lattice Qt. We use the entropy method of Kahn to show that log(L(Qt)) 2t = log ( t bt/2c ) − 3 2 log e + o(1), where the logarithms are base 2. We also find the exact maximum number of linear extensions of a d-regular bipartite order on n elements, in the case when n is a multiple of 2d.

We prove the following theorem. Let L be any link. There is some N = NL such that every straight-edge embedding of the complete bipartite graph KN,N contains a finite union of cycles having link type L. This result builds on the ideas of S. Negami, who proved the analogous result for complete graphs. Most of our motivation for this paper is to give a simpler proof of Negami’s Theorem.

Web content quality evaluation is crucial to various web content processing applications. Bagging has a powerful classification capacity by combining multiple classifiers. In this study, similar to Bagging, multiple pairwise bipartite ranking learners are combined to solve the multipartite ranking problems for web content quality evaluation. Both encoding and decoding mechanisms are used to com...