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On a graph coloring problem arising from discrete tomography

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On the Turan number of ordered forests

Gábor Tardos, Istvan Tomon, Dániel József Korándi

An ordered graph H is a simple graph with a linear order on its vertex set. The corresponding Turan problem, first studied by Pach and Tardos, asks for the maximum number ex(

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

Stability results for vertex Turatn problems in Kneser graphs

Abhishek Methuku

The vertex set of the Kneser graph K(n, k) is V = (([n])(k)) and two vertices are adjacent if the corresponding sets are disjoint. For any graph F, the largest size of a vertex set U subset of V such that K(n, k)[U] is F-free, was recently determined by Al ...

ELECTRONIC JOURNAL OF COMBINATORICS2019

Generalized Turan Problems For Even Cycles

Abhishek Methuku

Given a graph H and a set of graphs F, let ex(n, H, F) denote the maximum possible number of copies of H in an T-free graph on n vertices. We investigate the function ex(n, H, F), when H and members of F are cycles. Let C-k denote the cycle of length k and ...

2019

Ramsey-Turan numbers for semi-algebraic graphs

János Pach

A semi-algebraic graph G = (V, E) is a graph where the vertices are points in R-d, and the edge set E is defined by a semi-algebraic relation of constant complexity on V. In this note, we establish the following Ramsey-Turan theorem: for every integer p >= ...

ELECTRONIC JOURNAL OF COMBINATORICS2018

Independence number of generalized Petersen graphs

Javad Ebrahimi Boroojeni

Determining the size of a maximum independent set of a graph G, denoted by alpha(G), is an NP-hard problem. Therefore many attempts are made to find upper and lower bounds, or exact values of alpha(G) for special classes of graphs. This paper is aimed towa ...

Charles Babbage Res Ctr2016

Scaling a Reliable Distributed System

Alexandre David Olivier Maurer

We consider the problem of reliably connecting an arbitrarily large set of computers (nodes) with communication channels. Reliability means here the ability, for any two nodes, to remain connected (i.e., their ability to communicate) with probability at le ...

LPD EPFL2016

PrefEdge: SSD Prefetcher for Large-Scale Graph Traversal

Amitabha Roy

Mining large graphs has now become an important aspect of multiple diverse applications and a number of computer systems have been proposed to provide runtime support. Recent interest in this area has led to the construction of single machine graph computa ...

2014

Triangle-free intersection graphs of line segments with large chromatic number

Bartosz Maria Walczak, Michal Lason

In the 1970s Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer k we construct a triangle-free fam ...

Academic Press Inc Elsevier Science2014

Coloring Intersection Graphs of Arc-Connected Sets in the Plane

Bartosz Maria Walczak, Michal Lason

A family of sets in the plane is simple if the intersection of any subfamily is arc-connected, and it is pierced by a line L if the intersection of any member with L is a nonempty segment. It is proved that the intersection graphs of simple families of com ...

Springer2014

Coloring Triangle-Free Rectangular Frame Intersection Graphs with O(loglogn) Colors

Bartosz Maria Walczak

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). ...

2013