Concept

Lemme des poignées de main

Publications associées (20)

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Adjacent Crossings Do Matter

Radoslav Fulek

In a drawing of a graph, two edges form an odd pair if they cross each other an odd number of times. A pair of edges is independent if they share no endpoint. For a graph G, let ocr(G) be the smallest number of odd pairs in a drawing of G and let iocr(G) b ...

Springer-Verlag Berlin2011

Approximating Graphic TSP by Matchings

Ola Nils Anders Svensson

We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leadi ...

IEEE Computer Society2011

A bipartite strengthening of the Crossing Lemma

János Pach

Let G = (V, E) be a graph with n vertices and m >= 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Omega(m(3)/n(2)) pairs of crossing edges; or equivalently, there is an edge that crosses Omega(m(2)/n(2)) other edges. ...

2010

Split-critical and uniquely split-colorable graphs

Dominique de Werra, Bernard Ries, Tinaz Ekim

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 ...

2010

From L. Euler to D. König

Dominique de Werra

Starting from the famous Konigsberg bridge problem which Euler described in 1736, we intend to show that some results obtained 180 years later by Konig are very close to Euler's discoveries. ...

2009

Network coding for undirected information exchange

Christina Fragouli, Suhas Diggavi

We consider the information exchange problem where each in a set of terminals transmits information to all other terminals in the set, over an undirected network. We show that the design of only a single network code for multicasting is sufficient to achie ...

2009

Explicit construction of self-dual integral normal bases for the square-root of the inverse different

Erik Jarl Pickett

Let K be a finite extension of Q(p), let L/K be a finite abelian Galois extension of odd degree and let D-L be the valuation ring of L. We define A(L/K) to be the unique fractional D-L-ideal with square equal to the inverse different of L/K. For p an odd p ...

2009

Parity-regular Steinhaus graphs

Maxime Augier

Steinhaus graphs on n vertices are certain simple graphs in bijective correspondence with binary {0,1}-sequences of length n-1. A conjecture of Dymacek in 1979 states that the only nontrivial regular Steinhaus graphs are those corresponding to the periodic ...

American Mathematical Society2008

Generalized vertex coloring problems using split graphs

Tinaz Ekim

Graph theory experienced a remarkable increase of interest among the scientific community during the last decades. The vertex coloring problem (Min Coloring) deserves a particular attention rince it has been able to capture a wide variety of applications. ...

EPFL2006

A statistical physics perspective of complex networks

Thomas Petermann

A statistical physics perspective of complex networks: from the architecture of the Internet and the brain to the spreading of an epidemic Statistical physics has revealed itself as the ideal framework to describe large networks appearing in a variety of d ...

EPFL2005