18 papers
The maximum sum of sizes of cross-intersecting families of subsets of a set
Peter Borg, Carl Feghali
A set of sets is called a family. Two families and of sets are said to be cross-intersecting if each member of intersects each member of $…
A simple proof of Talbot's theorem for intersecting separated sets
Peter Borg, Carl Feghali
A subset of is -separated if, when the elements of are considered on a circle, between any two elements of there are at least elements…
A Thomassen-type method for planar graph recoloring
Zdeněk Dvořák, Carl Feghali
The reconfiguration graph for the -colorings of a graph has as vertices all possible -colorings of and two colorings are adjacent if they differ in the color…
An update on reconfiguring -colorings of planar graphs
Zdeněk Dvořák, Carl Feghali
The reconfiguration graph for the -colorings of a graph has as vertex set the set of all possible proper -colorings of and two colorings are adjacent if they…
Intersecting families, signed sets, and injection
Carl Feghali
Let be integers, and let be the family of -signed -sets on given by $$ \mathcal{S}_{n, k, r} = \Big\{\{(x_1, a_1), \dot…
An Erdős-Ko-Rado Theorem for unions of length 2 paths
Carl Feghali, Glenn Hurlbert, Vikram Kamat
A family of sets is intersecting if any two sets in the family intersect. Given a graph and an integer , let denote the family of independent se…