11 papers
Edge mappings of graphs: Ramsey type parameters
Yair Caro, Balázs Patkós, Zsolt Tuza +1
In this paper, we launch a systematic study of parameters concerning edge mappings of graphs. Inspired by Ramsey's theorem, the quantity is defined to be the smallest inte…
On zero-sum Ramsey numbers modulo 3
Yair Caro, Xandru Mifsud
We start with a systematic study of the zero-sum Ramsey numbers. For a graph with edges, the zero-sum Ramsey number is defined as the smallest positive i…
Induced/Incomparable versus Ramsey
Yair Caro, Zsolt Tuza, Christina Zarb
We consider the following problem: Let and be two graphs on vertices and assume . We say that and are incomparable if neither nor contains the…
Independence, induced subgraphs, and domination in -free graphs
Yair Caro, Randy Davila, Michael A. Henning +1
Let be a graph and a family of graphs. Define as the maximum order of any induced subgraph of that belongs to the family .…
Results on three problems on isolation of graphs
Peter Borg, Yair Caro
The graph isolation problem was introduced by Caro and Hansberg in 2015. It is a vast generalization of the classical graph domination problem and its study is expanding rapidly. I…
The odd independence number of graphs, I: Foundations and classical classes
Yair Caro, Mirko Petruševski, Riste Škrekovski +1
An odd independent set in a graph is an independent set of vertices such that, for every vertex , either or $|N(v) \cap…