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On some graph classes related to perfect graphs: A survey
(Elsevier, 2020)
Perfect graphs form a well-known class of graphs introduced by Berge in the 1960s in terms of a min-max type equality involving two famous graph parameters. In this work, we survey certain variants and subclasses of perfect ...
On some graph classes related to perfect graphs: A survey
(Elsevier B.V., 2020)
© 2019 Elsevier B.V.Perfect graphs form a well-known class of graphs introduced by Berge in the 1960s in terms of a min–max type equality involving two famous graph parameters. In this work, we survey certain variants and ...
p-BOX: A new graph model
(2015)
In this document, we study 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. Two vertices are connected by an edge if and only if its ...
Coordinated graphs and clique graphs of clique-Helly perfect graphs
(2007)
A new class of graphs related to perfect graphs is defined in this work: coordinated graphs. A graph G is coordinated if the cardinality of a maximum set of cliques of H with a common vertex is equal to the cardinality of ...
On probe 2-clique graphs and probe diamond-free graphs
(Discrete Mathematics and Theoretical Computer Science, 2015)
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 ...
Colouring exact distance graphs of chordal graphs
(Elsevier, 2020)
For a graph G = (V, E) and positive integer p, the exact distance-p graph G([hp]) is the graph with vertex set V and with an edge between vertices x and y if and only if x and y have distance p. Recently, there has been ...
Graphs admitting antimagic labeling for arbitrary sets of positive integers
(Elsevier, 2017)
A connected graph G=(V,E) with m edges is called universal antimagic if for each set B of m positive integers there is an bijective function f:E→B such that the function f˜:V→N defined at each vertex v as the sum of all ...
On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
(Elsevier B.V., 2018)
Golumbic, Lipshteyn and Stern [12] proved that every graph can be represented as the edge
intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex
of the graph a nontrivial path on a ...
Graphs admitting antimagic labeling for arbitrary sets of positive numbers
(Elsevier, 2020)
Hartsfield and Ringel in 1990 conjectured that any connected graph with q >= 2 edges has an edge labeling f with labels in the set {1,..., q}, such that for every two distinct vertices u and v, f(u) not equal= f(v), where ...
Structural results on circular-arc graphs and circle graphs: A survey and the main open problems
(Elsevier, 2014)
Circular-arc graphs are the intersection graphs of open arcs on a circle. Circle graphs are
the intersection graphs of chords on a circle. These graph classes have been the subject
of much study for many years and numerous ...