Graph classes and forbidden patterns on three vertices

@article{Feuilloley2021GraphCA,
  title={Graph classes and forbidden patterns on three vertices},
  author={Laurent Feuilloley and Michel Habib},
  journal={SIAM J. Discret. Math.},
  year={2021},
  volume={35},
  pages={55-90}
}
This paper deals with graph classes characterization and recognition. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs. Unfortunately this strategy usually does not lead to an efficient recognition algorithm. On the other hand, many graph classes can be efficiently recognized by techniques based on some interesting orderings of the nodes, such as the ones given by traversals. We study specifically graph classes that have an ordering avoiding… 

Figures and Tables from this paper

Classifying grounded intersection graphs via ordered forbidden patterns
TLDR
It is claimed that forbidden patterns are a useful tool to classify grounded intersection graphs, and the correspondence between a pattern on four vertices and grounded rectangle graphs is not an isolated phenomenon.
Describing hereditary properties by forbidden circular orderings
Each hereditary property can be characterized by its set of minimal obstructions; these sets are often unknown, or known but infinite. By allowing extra structure it is sometimes possible to describe
Intersection models and forbidden pattern characterizations for 2-thin and proper 2-thin graphs
TLDR
This work proves that the proper thinness of a graph is at most its bandwidth, for graphs with at least one edge, and characterizations of 2-thin and 2-proper thin graphs as intersection graphs of rectangles in the plane with sides parallel to the Cartesian axes and other specific conditions.
Introduction to local certification
TLDR
This paper is an introduction to the domain of local certification, giving an overview of the history, the techniques and the current research directions.
About Some Hereditary Classes of Graphs : Algorithms - Structure - Coloration
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and
Mental creation and physical creation of the future of ESS
  • H. Kamabe
  • Computer Science
    IEICE ESS Fundamentals Review
  • 2022
Machine learning has made remarkable progress, and a wide range of research has been conducted from theoretical and practical perspectives. However, the expansion of machine learning applications has
Local certification in distributed computing: error-sensitivity, uniformity, redundancy, and interactivity. (Certification locale en calcul distribué : sensibilité aux erreurs, uniformité, redondance et interactivité)
Cette these porte sur la notion de certification locale, un sujet central en decision distribuee, un domaine du calcul distribue. Le mecanisme de la decision distribuee consiste, pour les nœuds d'un

References

SHOWING 1-10 OF 115 REFERENCES
Maximum Induced Matchings for Chordal Graphs in Linear Time
TLDR
This paper gives an algorithm which is based on perfect elimination order and LexBFS for the MIM problem on chordal graphs and shows that it is solvable in polynomial time for various classes of graphs.
On the Computational Complexity of Ordered Subgraph Recognition
TLDR
It is conjecture that for any 2-connected graph G, G ≠ Kk, (G, <)ORD is NP-complete, verified for almost all 2- connected graphs.
A Characterization of Comparability Graphs and of Interval Graphs
Let < be a non-reflexive partial ordering defined on a set P. Let G(P, <) be the undirected graph whose vertices are the elements of P, and whose edges (a, b) connect vertices for which either a < b
A Unified View of Graph Searching
TLDR
This paper unifies the view of graph search algorithms by showing simple, closely related characterizations of various well-known search paradigms, including BFS and DFS, and these characterizations naturally lead to other search paradigsms, namely, maximal neighborhood search and LexDFS.
Algorithmic Aspects of Vertex Elimination on Graphs
TLDR
A graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric positive definite systems of linear equations is considered, and it is conjecture that the problem of finding a minimum ordering is NP-complete.
The strong perfect graph theorem
In 1960 Berge came up with the concept of perfect graphs, and in doing so, conjectured some characteristics about them. A perfect graph is a graph in which the chromatic number of every induced
Berge trigraphs
TLDR
The parts that differ significantly from the proof of the decomposition theorem for Berge graphs are presented, and only in the case needed for the application.
p-Box: A new graph model
TLDR
This document studies the scope of the following graph model: each vertex is assigned to a box in ℝd and to a representative element that belongs to that box and gives both, a combinatorial and an intersection characterization of the model.
On the Power of Graph Searching for Cocomparability Graphs
TLDR
This paper presents a characterization of the searches that preserve cocomp orderings when used as a “$^+$” sweep and illustrates these techniques by describing a very simple certifying algorithm for the maximum independent set problem as well as a simple permutation graph recognition algorithm.
Asteroidal Triple-Free Graphs
TLDR
This paper argues that the property of being AT-free is what is enforcing the linear ordering of the vertex sets of asteroidal triple-free graphs and presents various structural properties and characterizations of AT- free graphs.
...
...