G. Sárközy

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20242026

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4 papers · 1 filter

math.CO2026

Bounded diameter covering of 2-colored complete bipartite graphs

Louis DeBiasio, András Gyárfás, Gábor N. Sárközy

Related to a bounded-diameter bipartite analogue of the Henderson--Ryser conjecture, DeBiasio, Kamel, McCourt, and Sheats proved that the vertices of every $2$ -colored complete bip…

math.CO2025

Proper edge colorings of planar graphs with rainbow $C_{4}$ -s

AndrÃ¡s GyÃ¡rfÃ¡s, Ryan R. Martin, MiklÃ³s RuszinkÃ³ +1

We call a proper edge coloring of a graph $G$ a B-coloring if every 4-cycle of $G$ is colored with four different colors. Let $q_{B} (G)$ denote the smallest number of colors needed f…

math.CO2025

2-reachable subsets in two-colored graphs

Andras Gyarfas, Gabor N. Sarkozy

A subset $X$ of vertices in a graph $G$ is a {\em diameter 2 subset} if the distance of any two vertices of $X$ is at most two {\em in $G [X]$ }. Relaxing this notion, a subset $X$ o…

math.CO2024

Clique covers of complete graphs and piercing multitrack intervals

JÃ¡nos BarÃ¡t, AndrÃ¡s GyÃ¡rfÃ¡s, GÃ¡bor N. SÃ¡rkÃ¶zy

Assume that $R_{1}, R_{2}, \dots, R_{t}$ are disjoint parallel lines in the plane. A $t$ -interval (or $t$ -track interval) is a set that can be written as the union of $t$ closed intervals,…

Bounded diameter covering of 2-colored complete bipartite graphs

Proper edge colorings of planar graphs with rainbow C4​-s

2-reachable subsets in two-colored graphs

Clique covers of complete graphs and piercing multitrack intervals

Proper edge colorings of planar graphs with rainbow $C_{4}$ -s