6 papers · 1 filter
Star Coloring on Some Subclasses of Chordal Graphs
Germán Benítez-Bobadilla, Fernando Esteban Contreras-Mendoza, César Hernández-Cruz +2
A star coloring of a graph is a proper coloring in which no path on four vertices is bicolored. The star chromatic number is the minimum number of colors in a st…
Maya-Tupi graphs: a generalization of split graphs
Júlio Araújo, César Hernández-Cruz, Cláudia Linhares Sales
We define the family of Maya-Tupi graphs as those graphs that admit a partition of their vertex sets such that induces a complete multipartite graph where each part has…
Minimal obstructions to -polar cographs
Pavol Hell, César Hernández-Cruz, Cláudia Linhares Sales
A graph is a cograph if it is -free. A -polar partition of a graph is a partition of the set of vertices of into parts and such that the subgraph induced by…
Proper Orientations of Planar Bipartite Graphs
Fiachra Knox, Sebastián González Hermosillo de la Maza, Bojan Mohar +1
An orientation of a graph is proper if any two adjacent vertices have different indegrees. The proper orientation number of a graph is the minimum of…
The b-continuity of graphs with large girth
Ana Silva, Cláudia Linhares-Sales
A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to each other color class. The b-chromatic number of is…
Dirac's theorem on simplicial matroids
Raul Cordovil, Manoel Lemos, Claudia Linhares Sales
We introduce the notion of k-hyperclique complexes, i.e., the largest simplicial complexes on the set [n] with a fixed k-skeleton. These simplicial complexes are a higher-dimension…