Concept

Comparability graph

In graph theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability graph is an undirected graph that connects pairs of elements that are not comparable to each other in a partial order. For any strict partially ordered set (S,

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https://en.wikipedia.org/wiki/Comparability_graph

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Pascal Fua received an engineering degree from Ecole Polytechnique, Paris, in 1984 and the Ph.D. degree in Computer Science from the University of Orsay in 1989. He then worked at SRI International and INRIA Sophia-Antipolis as a Computer Scientist. He joined EPFL in 1996 where he is now a Professor in the School of Computer and Communication Science and heads the Computer Vision Laboratory. His research interests include shape modeling and motion recovery from images, analysis of microscopy images, and Augmented Reality. His research interests include shape modeling and motion recovery from images, analysis of microscopy images, and machine learning. He has (co)authored over 300 publications in refereed journals and conferences. He is an IEEE Fellow and has been an Associate Editor of IEEE journal Transactions for Pattern Analysis and Machine Intelligence. He often serves as program committee member, area chair, and program chair of major vision conferences and has cofounded three spinoff companies (Pix4D, PlayfulVision, and NeuralConcept).

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Robert Dalang, né en 1961, a reçu le diplôme de Mathématicien-EPFL en 1983 et est lauréat du Prix Dommer. Il passe l'année 1985-86 à Cornell University (USA) comme chercheur invité. Il obtient le doctorat au Département de mathématiques de l'EPFL en 1987. Son domaine de spécialisation est la théorie des processeurs stochastiques. En 1987, Robert Dalang est nommé professeur assistant au Département de statistiques de l'Université de Californie à Berkeley (USA). En 1988, il reçoit une bourse post-doctorale du Fonds national scientifique américain et effectue des recherches sur les propriétés markoviennes de processus stochastiques à plusieurs paramètres. En 1990, il est nommé à Tufts University (Boston, USA). Il est promu professeur associé en mai 1993. Une partie importante de ses recherches se font dans le cadre de contrats avec le Fonds national scientifique américain et l'Office de la recherche de l'armée américaine. En collaboration avec le Prof. R. Cairoli du Département de mathématiques de l'EPFL, il a écrit un livre sur l'optimisation stochastique séquentielle publié en 1996 aux éditions John Wiley. M. Dalang est nommé professeur extraordinaire de probabilités au Département de mathématiques en 1995. Il y poursuit des travaux de recherche en processus stochastiques et probabilité appliquée et participe à l'enseignement des processus stochastiques, de la théorie des probabilités et des cours de mathématiques aux sections d'ingénieurs. Il dirige régulièrement des thèses de doctorats, est éditeur de plusieurs journaux de recherche mathématique et travail en collaboration avec des chercheurs de plusieurs universités européennes et américaines.

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Official source

https://en.wikipedia.org/wiki/Comparability_graph

About this result

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

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A well-known theorem of Nikiforov asserts that any graph with a positive

K_{r}

-density contains a logarithmic blowup of

K_r

. In this paper, we explore variants of Nikiforov’s result in the following form. Given

r,t\in \mathbb{N}

, when a positive

K_{r}

-density implies the existence of a significantly larger (with almost linear size) blowup of

K_t

? Our results include: • For an

n

-vertex ordered graph

G

with no induced monotone path

P_{6}

, if its complement

\overline {G}

has positive t

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