scholarly journals Balancedness of subclasses of circular-arc graphs

2014 ◽  
Vol Vol. 16 no. 3 (Graph Theory) ◽  
Author(s):  
Flavia Bonomo ◽  
Guillermo Duran ◽  
Martın D. Safe ◽  
Annegret K. Wagler
Keyword(s):  
Incidence Matrix ◽  
Perfect Graphs ◽  
Induced Subgraphs ◽  
Circular Arc ◽  
Forbidden Induced Subgraphs ◽  
Odd Order ◽  
International Audience ◽  
Circular Arc Graphs ◽  
Balanced Graphs

Graph Theory International audience A graph is balanced if its clique-vertex incidence matrix contains no square submatrix of odd order with exactly two ones per row and per column. There is a characterization of balanced graphs by forbidden induced subgraphs, but no characterization by mininal forbidden induced subgraphs is known, not even for the case of circular-arc graphs. A circular-arc graph is the intersection graph of a family of arcs on a circle. In this work, we characterize when a given graph G is balanced in terms of minimal forbidden induced subgraphs, by restricting the analysis to the case where G belongs to certain classes of circular-arc graphs, including Helly circular-arc graphs, claw-free circular-arc graphs, and gem-free circular-arc graphs. In the case of gem-free circular-arc graphs, analogous characterizations are derived for two superclasses of balanced graphs: clique-perfect graphs and coordinated graphs.

scholarly journals A Characterization of 2-Tree Proper Interval 3-Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
David E. Brown ◽  
Breeann M. Flesch
Keyword(s):  
Nonempty Intersection ◽  
Intersection Graph ◽  
Induced Subgraphs ◽  
Forbidden Induced Subgraphs ◽  
Different Color

An interval p-graph is the intersection graph of a collection of intervals which have been colored with p different colors with edges corresponding to nonempty intersection of intervals from different color classes. We characterize the class of 2-trees which are interval 3-graphs via a list of three graphs and three infinite families of forbidden induced subgraphs.

scholarly journals Isomorphism of graph classes related to the circular-ones property

2013 ◽  
Vol Vol. 15 no. 1 (Discrete Algorithms) ◽  
Author(s):  
Andrew R. Curtis ◽  
Min Chih Lin ◽  
Ross M. Mcconnell ◽  
Yahav Nussbaum ◽  
Francisco Juan Soulignac ◽  
...  
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Circular Arc ◽  
Graph Classes ◽  
Discrete Algorithms ◽  
International Audience ◽  
Related Graph ◽  
Circular Arc Graphs ◽  
Proper Circular Arc Graphs

Discrete Algorithms International audience We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. Our algorithm is similar to the isomorphism algorithm for interval graphs of Lueker and Booth, but works on PC trees, which are unrooted and have a cyclic nature, rather than with PQ trees, which are rooted. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, Γ circular-arc graphs, proper circular-arc graphs and convex-round graphs.

scholarly journals Partial characterizations of clique-perfect graphs II: Diamond-free and Helly circular-arc graphs

2009 ◽  
Vol 309 (11) ◽  
pp. 3485-3499 ◽  
Author(s):  
Flavia Bonomo ◽  
Maria Chudnovsky ◽  
Guillermo Durán
Keyword(s):  
Perfect Graphs ◽  
Circular Arc ◽  
Circular Arc Graphs

scholarly journals On forbidden induced subgraphs for K1,3-free perfect graphs

2019 ◽  
Vol 342 (6) ◽  
pp. 1602-1608
Author(s):  
Christoph Brause ◽  
Přemysl Holub ◽  
Adam Kabela ◽  
Zdeněk Ryjáček ◽  
Ingo Schiermeyer ◽  
...  
Keyword(s):  
Perfect Graphs ◽  
Induced Subgraphs ◽  
Forbidden Induced Subgraphs

scholarly journals A new characterization and a recognition algorithm of Lucas cubes

2013 ◽  
Vol Vol. 15 no. 3 (Graph Theory) ◽  
Author(s):  
Andrej Taranenko
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Linear Time ◽  
Recognition Algorithm ◽  
Induced Subgraphs ◽  
Fibonacci Cube ◽  
Vertex Set ◽  
International Audience ◽  
Binary Strings

Graph Theory International audience Fibonacci and Lucas cubes are induced subgraphs of hypercubes obtained by excluding certain binary strings from the vertex set. They appear as models for interconnection networks, as well as in chemistry. We derive a characterization of Lucas cubes that is based on a peripheral expansion of a unique convex subgraph of an appropriate Fibonacci cube. This serves as the foundation for a recognition algorithm of Lucas cubes that runs in linear time.

scholarly journals Linear Time Recognition of P4-Indifferent Graphs

1999 ◽  
Vol 6 (38) ◽  
Author(s):  
Romeo Rizzi
Keyword(s):  
Key Words ◽  
Linear Time ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Induced Subgraphs ◽  
Modular Decomposition ◽  
Forbidden Induced Subgraphs ◽  
Chordless Path

<p>A simple graph is P4-indifferent if it admits a total order < on<br />its nodes such that every chordless path with nodes a, b, c, d and edges<br />ab, bc, cd has a < b < c < d or a > b > c > d. P4-indifferent graphs generalize<br /> indifferent graphs and are perfectly orderable. Recently, Hoang,<br />Maray and Noy gave a characterization of P4-indifferent graphs in<br />terms of forbidden induced subgraphs. We clarify their proof and describe<br /> a linear time algorithm to recognize P4-indifferent graphs. When<br />the input is a P4-indifferent graph, then the algorithm computes an order < as above.</p><p>Key words: P4-indifference, linear time, recognition, modular decomposition.</p><p> </p>

scholarly journals Clique cycle transversals in graphs with few P₄'s

2013 ◽  
Vol Vol. 15 no. 3 (Graph Theory) ◽  
Author(s):  
Raquel Bravo ◽  
Sulamita Klein ◽  
Loana Tito Nogueira ◽  
Fábio Protti
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Finite Family ◽  
Feedback Vertex Set ◽  
Induced Subgraphs ◽  
Complete Subgraph ◽  
Forbidden Induced Subgraphs ◽  
Vertex Set ◽  
International Audience ◽  
Acyclic Subgraph

Graph Theory International audience A graph is extended P4-laden if each of its induced subgraphs with at most six vertices that contains more than two induced P4's is 2K2,C4-free. A cycle transversal (or feedback vertex set) of a graph G is a subset T ⊆ V (G) such that T ∩ V (C) 6= ∅ for every cycle C of G; if, in addition, T is a clique, then T is a clique cycle transversal (cct). Finding a cct in a graph G is equivalent to partitioning V (G) into subsets C and F such that C induces a complete subgraph and F an acyclic subgraph. This work considers the problem of characterizing extended P4-laden graphs admitting a cct. We characterize such graphs by means of a finite family of forbidden induced subgraphs, and present a linear-time algorithm to recognize them.

scholarly journals On probe 2-clique graphs and probe diamond-free graphs

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Flavia Bonomo ◽  
Celina M. H. Figueiredo ◽  
Guillermo Duran ◽  
Luciano N. Grippo ◽  
Martín D. Safe ◽  
...  
Keyword(s):  
Graph Theory ◽  
Recognition Algorithm ◽  
Chordal Graphs ◽  
Stable Set ◽  
Induced Subgraphs ◽  
Forbidden Induced Subgraphs ◽  
Block Graphs ◽  
International Audience ◽  
Clique Graphs ◽  
Probe Block

Graph Theory International audience Given a class G of graphs, probe G graphs are defined as follows. A graph G is probe G if there exists a partition of its vertices into a set of probe vertices and a stable set of nonprobe vertices in such a way that non-edges of G, whose endpoints are nonprobe vertices, can be added so that the resulting graph belongs to G. We investigate probe 2-clique graphs and probe diamond-free graphs. For probe 2-clique graphs, we present a polynomial-time recognition algorithm. Probe diamond-free graphs are characterized by minimal forbidden induced subgraphs. As a by-product, it is proved that the class of probe block graphs is the intersection between the classes of chordal graphs and probe diamond-free graphs.

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