Z. Tuza

activity

20242026

collaborators

10 papers

math.MG2026

Covering a square by congruent squares

GyÃ¶rgy DÃ³sa, Zsolt LÃ¡ngi, Zsolt Tuza

The main goal of this paper is to address the following problem: given a positive integer $n$ , find the largest value $S (n)$ such that a square of edge length $S (n)$ in the Euclide…

math.CO2026

Induced/Incomparable versus Ramsey

Yair Caro, Zsolt Tuza, Christina Zarb

We consider the following problem: Let $H$ and $F$ be two graphs on $k$ vertices and assume $F \neq = H$ . We say that $H$ and $F$ are incomparable if neither $F$ nor $H$ contains the…

math.CO2026

The odd independence number of graphs, I: Foundations and classical classes

Yair Caro, Mirko PetruÅ¡evski, Riste Å krekovski +1

An odd independent set $S$ in a graph $G = (V, E)$ is an independent set of vertices such that, for every vertex $v \in V ∖ S$ , either $N (v) \cap S = \emptyset$ or $|N(v) \cap…

math.CO2026

Nordhaus-Gaddum-type theorems for maximum average degree

Yair Caro, Zsolt Tuza

A $k$ -decomposition $(G_{1}, \dots, G_{k})$ of a graph $G$ is a partition of its edge set into $k$ spanning subgraphs $G_{1}, \dots, G_{k}$ . The classical theorem of Nordhaus and Gaddum bounds…

math.CO2025

The odd independence number of graphs, II: Finite and infinite grids and chessboard graphs

Yair Caro, Mirko PetruÅ¡evski, Riste Å krekovski +1

An odd independent set $S$ in a graph $G = (V, E)$ is an independent set of vertices such that, for every vertex $v \in V ∖ S$ , either $N (v) \cap S = \emptyset$ or $|N(v) \cap…

math.LO2025

Transposition of variables is hard to describe

The function $p_{x y}$ that interchanges two logical variables $x, y$ in formulas is hard to describe in the following sense. Let $F$ denote the Lindenbaum-Tarski formula-algebra of…