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We prove that for any triangle-free intersection graph of n axis-parallel line segments in the plane, the independence number alpha of this graph is at least alpha n/4+ohm(root n). We complement this with a construction of a graph in this class satisfying ...
A clique covering of a graph G is a set of cliques of G such that any edge of G is contained in one of these cliques, and the weight of a clique covering is the sum of the sizes of the cliques in it. The sigma clique cover number scc(G) of a graph G, is de ...
An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n.Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed p ...
A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only up to Markov equi ...
Given a graph G with nonnegative node labels w, a multiset of stable sets S_1,...,S_k\subseteq V(G) such that each vertex v \in V(G) is contained in w(v) many of these stable sets is called a weighted coloring. The weighted coloring number \chi_w(G) is the ...
The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs defined by geometric representations and competitivity analysis of on-line algorithms. This connection became apparent after the recent construction ...
Given a collection C of curves in the plane, its string graph is defined as the graph with vertex set C, in which two curves in C are adjacent if and only if they intersect. Given a partially ordered set (P,
Recently, Pawlik et al. have shown that triangle-free intersection graphs of line segments in the plane can have arbitrarily large chromatic number. Specifically, they construct triangle-free segment intersection graphs with chromatic number Θ(log log n). ...
The split-coloring problem is a generalized vertex coloring problem where we partition the vertices into a minimum number of split graphs. In this paper, we study some notions which are extensively studied for the usual vertex coloring and the cocoloring p ...
Computing the weighted coloring number of graphs is a classical topic in combinatorics and graph theory. Recently these problems have again attracted a lot of attention for the class of quasi-line graphs and more specifically fuzzy circular interval graphs ...
