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Improved data structures for fully dynamic biconnectivity

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Coloring Relatives of Interval Overlap Graphs via On-line Games

Bartosz Maria Walczak

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 ...

Springer-Verlag Berlin2014

Drawing Planar Graphs Of Bounded Degree With Few Slopes

János Pach, Balázs Keszegh, Doemoetoer Palvoelgyi

We settle a problem of Dujmovic, Eppstein, Suderman, and Wood by showing that there exists a function f with the property that every planar graph G with maximum degree d admits a drawing with noncrossing straight-line edges, using at most f(d) different sl ...

Siam Publications2013

On The Queue Number Of Planar Graphs

János Pach, Fabrizio Frati

We prove that planar graphs have O(log(2) n) queue number, thus improving upon the previous O(root n) upper bound. Consequently, planar graphs admit three-dimensional straight-line crossing-free grid drawings in O(n log(8) n) volume, thus improving upon th ...

Siam Publications2013

Lower bounds on the obstacle number of graphs

János Pach, Doemoetoer Palvoelgyi, Padmini Mukkamala

Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if and only if the corresponding points can be con ...

2012

Efficient graph planarization in sensor networks and local routing algorithm

Florian Huc

In this paper, we propose an efficient planarization algorithm and a routing algorithm dedicated to Unit Disk Graphs whose nodes are localized using the Virtual Raw Anchor Coordinate system (VRAC). Our first algorithm computes a planar 2-spanner under ligh ...

Ieee2012

Disjoint homometric sets in graphs

János Pach

Two subsets of vertices in a graph are called homometric if the multisets of distances determined by them are the same. Let h(n) denote the largest number h such that any connected graph of n vertices contains two disjoint homometric subsets of size h. It ...

2011

Drawing planar graphs of bounded degree with few slopes

János Pach, Balázs Keszegh, Doemoetoer Palvoelgyi

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2011

On the Page Number of Upward Planar Directed Acyclic Graphs

Radoslav Fulek, Fabrizio Frati, Andres Jacinto Ruiz Vargas

In this paper we study the page number of upward planar directed acyclic graphs. We prove that: (I) the page number of any n-vertex upward planar triangulation G whose every maximal 4-connected component has page number k is at most min {O(k log n), O(2(k) ...

Springer-Verlag Berlin2011

Hypergraphic LP Relaxations for Steiner Trees

David Pritchard

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this ...

Springer2010

Decomposition of Geometric Set Systems and Graphs

We study two decomposition problems in combinatorial geometry. The first part of the thesis deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-decomposable if there is a constant m such that any m-fold coveri ...

EPFL2010