Search Results - "de Mendez, Patrice Ossona"

Nowhere Dense Graph Classes and Dimension by Joret, Gwenaël, Micek, Piotr, Ossona de Mendez, Patrice, Wiechert, Veit

“…Nowhere dense graph classes provide one of the least restrictive notions of sparsity for graphs. Several equivalent characterizations of nowhere dense classes…”
Get full text

Defective Colouring of Graphs Excluding A Subgraph or Minor by Ossona De Mendez, Patrice, Oum, Sang-Il, Wood, David R.

“…Archdeacon (1987) proved that graphs embeddable on a fixed surface can be 3-coloured so that each colour class induces a subgraph of bounded maximum degree…”
Get full text

1-Subdivisions, the Fractional Chromatic Number and the Hall Ratio by Dvořák, Zdenĕk, de Mendez, Patrice Ossona, Wu, Hehui

“…The Hall ratio of a graph G is the maximum of | V ( H )|/ α ( H ) over all subgraphs H of G. It is easy to see that the Hall ratio of a graph is a lower bound…”
Get full text

Shrub-depth: Capturing Height of Dense Graphs by Ossona de Mendez, Patrice, Ganian, Robert, Hliněný, Petr, Nešetřil, Jaroslav, Obdrzalek, Jan

“…The recent increase of interest in the graph invariant called tree-depth and in its applications in algorithms and logic on graphs led to a natural question:…”
Get full text

A Note on Circular Chromatic Number of Graphs with Large Girth and Similar Problems by Nesetril, Jaroslav, Ossona de Mendez, Patrice

“…In this short note, we extend the result of Galluccio, Goddyn, and Hell, which states that graphs of large girth excluding a minor are nearly bipartite. We…”
Get full text

Local-global convergence, an analytic and structural approach by Jaroslav,  Nešetřil, Patrice, Ossona de Mendez

Get full text

Transducing paths in graph classes with unbounded shrubdepth by Ossona de Mendez, Patrice, Pilipczuk, Michał, Siebertz, Sebastian

“…Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic. We prove that a graph…”
Get full text

Modulo-counting first-order logic on bounded expansion classes by Nešetřil, Jaroslav, Ossona de Mendez, Patrice, Siebertz, Sebastian

“…We prove that, on bounded expansion classes, every first-order formula with modulo counting is equivalent, in a linear-time computable monadic expansion, to an…”
Get full text

Distributed domination on sparse graph classes by Heydt, Ozan, Kublenz, Simeon, Ossona de Mendez, Patrice, Siebertz, Sebastian, Vigny, Alexandre

“…We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on…”
Get full text

A few words about maps by Cori, Robert, Jiang, Yiting, Ossona de Mendez, Patrice, Rosenstiehl, Pierre

“…In this paper, we survey some properties, encoding, and bijections involving combinatorial maps, double occurrence words, and chord diagrams. We particularly…”
Get full text

On the generalised colouring numbers of graphs that exclude a fixed minor by van den Heuvel, Jan, de Mendez, Patrice Ossona, Quiroz, Daniel, Rabinovich, Roman, Siebertz, Sebastian

“…The generalised colouring numbers colr(G) and wcolr(G) were introduced by Kierstead and Yang as a generalisation of the usual colouring number, and have since…”
Get full text

Twin-width and generalized coloring numbers by Dreier, Jan, Gajarský, Jakub, Jiang, Yiting, Ossona de Mendez, Patrice, Raymond, Jean-Florent

“…In this paper, we prove that a graph G with no Ks,s-subgraph and twin-width d has r-admissibility and r-coloring numbers bounded from above by an exponential…”
Get full text

Classes of graphs with low complexity: The case of classes with bounded linear rankwidth by Nešetřil, Jaroslav, Ossona de Mendez, Patrice, Rabinovich, Roman, Siebertz, Sebastian

“…Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded linear rankwidth are MSO-transductions of paths – a result that shows a…”
Get full text

On nowhere dense graphs by Nešetřil, Jaroslav, Ossona de Mendez, Patrice

“…In this paper, we define and analyze the nowhere dense classes of graphs. This notion is a common generalization of proper minor closed classes, classes of…”
Get full text

From χ- to χ-bounded classes by Jiang, Yiting, Nešetřil, Jaroslav, Ossona de Mendez, Patrice

Get full text

On Low Tree-Depth Decompositions by Nešetřil, Jaroslav, Ossona de Mendez, Patrice

“…The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs…”
Get full text

Clustering Powers of Sparse Graphs by Nešetřil, Jaroslav, Ossona de Mendez, Patrice, Pilipczuk, Michał, Zhu, Xuding

“…We prove that if $G$ is a sparse graph — it belongs to a fixed class of bounded expansion $\mathcal{C}$ — and $d\in \mathbb{N}$ is fixed, then the $d$th power…”
Get full text

Characterisations and examples of graph classes with bounded expansion by Nešetřil, Jaroslav, Ossona de Mendez, Patrice, Wood, David R.

“…Classes with bounded expansion, which generalise classes that exclude a topological minor, have recently been introduced by Nešetřil and Ossona de Mendez…”
Get full text

Tree-depth, subgraph coloring and homomorphism bounds by Nešetřil, Jaroslav, Ossona de Mendez, Patrice

“…We define the notions tree-depth and upper chromatic number of a graph and show their relevance to local–global problems for graph partitions. In particular we…”
Get full text

EXISTENCE OF MODELING LIMITS FOR SEQUENCES OF SPARSE STRUCTURES by NEŠETŘIL, JAROSLAV, DEMENDEZ, PATRICE OSSONA

“…A sequence of graphs is FO-convergent if the probability of satisfaction of every first-order formula converges. A graph modeling is a graph, whose domain is a…”
Get full text