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Graph irregularity: discussion, graph extensions and new proposals
(Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica., 2015)
k-tuple colorings of the Cartesian product of graphs
(Elsevier Science, 2017-01)
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χk(G), is the smallest ...
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 ...
Helly EPT graphs on bounded degree trees: Characterization and recognition
(Elsevier Science, 2017-12)
The edge-intersection graph of a family of paths on a host tree is called an EPT graph. When the tree has maximum degree h, we say that the graph is [h,2,2]. If, in addition, the family of paths satisfies the Helly property, ...
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 ...
On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
(Sociedade Brasileira de Matematica, 2019-06)
A (0, 1)-matrix has the Consecutive Ones Property (C1P) for the rows if there is a permutation of its columns such that the ones in each row appear consecutively. We say a (0, 1)-matrix is nested if it has the consecutive ...