Kristóf Bérczi

Variations for Lovász’ Submodular Ideas

In [18], L. Lovasz provided simple and short proofs for two classic min-max theorems of graph theory by inventing basic techniques to handle sub- or supermodular functions. In this paper, we want to demonstrate that these ideas are alive after thirty years of their birth.

An algorithm for (n-3)-connectivity augmentation problem: Jump system approach

We consider the problem of making a given (k-1)-connected graph k-connected by adding a minimum number of new edges, which we call the k-connectivity augmentation problem. In this paper, we deal with the problem when k=n-3 where n is the number of vertices of the input graph. By considering the complement graph, the (n-3)-connectivity augmentation problem can be reduced to the problem of finding a maximum square-free 2-matching in a simple graph with maximum degree at most three. We give a polynomial-time algorithm to find a maximum square-free 2-matching in a simple graph with maximum degree at most three, which yields a polynomial-time algorithm for the (n-3)-connectivity augmentation problem. Our algorithm is based on the fact that the square-free 2-matchings are endowed with a matroid structure called a jump system. We also show that the weighted (n-3)-connectivity augmentation problem can be solved in polynomial time if the weights are induced by a function on the vertex set, whereas the problem is NP-hard for general weights.

Restricted b -matchings in degree-bounded graphs

We present a min-max formula and a polynomial time algorithm for a slight generalization of the following problem: in a simple undirected graph in which the degree of each node is at most t+1, find a maximum t-matching containing no member of a list

Supermodularity in Unweighted Graph Optimization II: Matroidal Term Rank Augmentation

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Supermodularity in Unweighted Graph Optimization III: Highly Connected Digraphs

of forbidden Kt,t and Kt+1 subgraphs. An analogous problem for bipartite graphs without degree bounds was solved by Makai [15], while the special case of finding a maximum square-free 2-matching in a subcubic graph was solved in [1].

Worst case bin packing for OTN electrical layer networks dimensioning

Rysers max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least

A tight √2-approximation for Linear 3-cut

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Making Bipartite Graphs DM-Irreducible

. In a previous paper by the authors, a generalization was developed for the case when the degrees are constrained by upper and lower bounds. Here two other extensions of Rysers theorem are discussed. The first one is a matroidal model, while the second one settles the augmentation version. In fact, the two directions shall be integrated into one single framework.

Arrival time dependent routing policies in public transport

By generalizing a recent result of Hong, Liu, and Lai on characterizing the degree-sequences of simple strongly connected directed graphs, a characterization is provided for degree-sequences of simple

Global and fixed-terminal cuts in digraphs

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