Resolution of Unmixed Bipartite Graphs
نویسندگان
چکیده
For an unmixed bipartite graph G we consider the lattice of vertex covers LG and compute depth, projective dimension and extremal Bettinumbers of R/I(G) in terms of this lattice.
منابع مشابه
A generalization of Villarreal's result for unmixed tripartite graphs
In this paper we give a characterization of unmixed tripartite graphs under certain conditions which is a generalization of a result of Villarreal on bipartite graphs. For bipartite graphs two different characterizations were given by Ravindra and Villarreal. We show that these two characterizations imply each other.
متن کاملUnmixed $r$-partite graphs
Unmixed bipartite graphs have been characterized by Ravindra and Villarreal independently. Our aim in this paper is to characterize unmixed $r$-partite graphs under a certain condition, which is a generalization of Villarreal's theorem on bipartite graphs. Also, we give some examples and counterexamples in relevance to this subject.
متن کاملUnmixed Bipartite Graphs and Sublattices of the Boolean Lattices
The correspondence between unmixed bipartite graphs and sublattices of the Boolean lattice is discussed. By using this correspondence, we show the existence of squarefree quadratic initial ideals of toric ideals arising from minimal vertex covers of unmixed bipartite graphs.
متن کاملRegularity, Depth and Arithmetic Rank of Bipartite Edge Ideals
We study minimal free resolutions of edge ideals of bipartite graphs. We associate a directed graph to a bipartite graph whose edge ideal is unmixed, and give expressions for the regularity and the depth of the edge ideal in terms of invariants of the directed graph. For some classes of unmixed edge ideals, we show that the arithmetic rank of the ideal equals projective dimension of its quotient.
متن کاملMETA-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کامل