M. Horňák

activity

20202022

K_{6} □ K_{q}

equals

2 q + 3

q \geq 41

is odd

2 citations · 5 across the 5 of their papers we have counts for

collaborators

5 papers

math.CO2022★ 1 cited

On the achromatic number of the Cartesian product of two complete graphs

Mirko Horňák

A vertex colouring $f : V (G) \to C$ of a graph $G$ is complete if for any $c_{1}, c_{2} \in C$ with $c_{1} \neq = c_{2}$ there are in $G$ adjacent vertices $v_{1}, v_{2}$ such that $f (v_{1}) = c_{1}$ and $f(v…

math.CO2021★ 1 cited

3-facial edge-coloring of plane graphs

Mirko Horňák, Borut Lužar, Kenny Štorgel

An $ℓ$ -facial edge-coloring of a plane graph is a coloring of its edges such that any two edges at distance at most $ℓ$ on a boundary walk of any face receive distinct colors…

math.CO2020

The achromatic number of $K_{6} □ K_{7}$ is $18$

Mirko Hornak

A vertex colouring $f : V (G) \to C$ of a graph $G$ is complete if for any two distinct colours $c_{1}, c_{2} \in C$ there is an edge ${v_{1}, v_{2}} \in E (G)$ such that $f (v_{i}) = c_{i}$ , $i = 1, 2$ . T…

math.CO2020★ 2 cited

The achromatic number of $K_{6} □ K_{q}$ equals $2 q + 3$ if $q \geq 41$ is odd

Mirko Hornak

Let $G$ be a graph and $C$ a finite set of colours. A vertex colouring $f : V (G) \to C$ is complete provided that for any two distinct colours $c_{1}, c_{2} \in C$ there is $v_{1} v_{2} \in E (G)$ …

math.CO2020★ 1 cited

The achromatic number of the Cartesian product of $K_{6}$ and $K_{q}$

Mirko Hornak

Let $G$ be a graph and $C$ a finite set of colours. A vertex colouring $f : V (G) \to C$ is complete if for any pair of distinct colours $c_{1}, c_{2} \in C$ one can find an edge $\{v_1,v_2\…

On the achromatic number of the Cartesian product of two complete graphs

3-facial edge-coloring of plane graphs

The achromatic number of K6​□K7​ is 18

The achromatic number of K6​□Kq​ equals 2q+3 if q≥41 is odd

The achromatic number of the Cartesian product of K6​ and Kq​

The achromatic number of $K_{6} □ K_{7}$ is $18$

The achromatic number of $K_{6} □ K_{q}$ equals $2 q + 3$ if $q \geq 41$ is odd

The achromatic number of the Cartesian product of $K_{6}$ and $K_{q}$