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Concept

Kuratowski's theorem

Related publications (9)

Atomic subgraphs and the statistical mechanics of networks

Sofia Charlotta Olhede

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extens ...

2021

Simple Realizability of Complete Abstract Topological Graphs Simplified

Jan Kyncl

An abstract topological graph (briefly an AT-graph) is a pair A = (G, X) where G = (V, E) is a graph and X. E2 is a set of pairs of its edges. The AT-graph A is simply realizable if G can be drawn in the plane so that each pair of edges from X crosses exac ...

SPRINGER2020

Graph Learning with Partial Observations: Role of Degree Concentration

Ali H. Sayed, Augusto José Rabelo Almeida Santos

In this work we consider the problem of learning an Erdos-Renyi graph over a diffusion network when: i) data from only a limited subset of nodes are available (partial observation); ii) and the inferential goal is to discover the graph of interconnections ...

IEEE2019

Time-resolved analysis of dynamic graphs: an extended Slepian design

Dimitri Nestor Alice Van De Ville, Raphaël Pierre Liégeois

Graphs are extensively used to represent networked data. In many applications, especially when considering large datasets, it is a desirable feature to focus the analysis onto specific subgraphs of interest. Slepian theory and its extension to graphs allow ...

SPIE-INT SOC OPTICAL ENGINEERING2019

On Simplices in Diameter Graphs in R-4

Andrei Kupavskii

A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...

Maik Nauka/Interperiodica/Springer2017

A Precise Threshold For Quasi-Ramsey Numbers

János Pach

We consider the variation of Ramsey numbers introduced by Erdos and Pach [J. Graph Theory, 7 (1983), pp. 137-147], where instead of seeking complete or independent sets we only seek a t-homogeneous set, a vertex subset that induces a subgraph of minimum de ...

SIAM Publications2015

Polarity of chordal graphs

Dominique de Werra, Tinaz Ekim

Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. They are defined by the existence of a certain partition of vertices, which is NP-complete to decide for general graphs. It has been recently proved that for cographs, th ...

2008

Polar cographs

Dominique de Werra, Tinaz Ekim

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s, k)-polar if there exists a partition A, B of its vertex set such that A induces a complete s-partite grap ...

Elsevier2008

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

Related publications (9)