N. Tokushige

collaborators

5 papers

math.CO2025

Burning numbers via eigenpolytopes -- Hamming graphs, Johnson graphs, and halved cubes

Hajime Tanaka, Norihide Tokushige

We give lower and upper bounds on the burning number of Hamming graphs, Johnson graphs, and halved cube graphs. For the lower bounds, we use the fact that $1$ -skeletons of the eige…

math.CO2025

Alon's transmitting problem and multicolor Beck--Spencer Lemma

Norihide Tokushige

The Hamming graph $H (n, q)$ is defined on the vertex set ${1, 2, \dots, q}^{n}$ and two vertices are adjacent if and only if they differ in precisely one coordinate. Alon (1992) prove…

math.CO2025

Extremal problems for intersecting families of subspaces with a measure

Hajime Tanaka, Norihide Tokushige

We introduce a measure for subspaces of a vector space over a $q$ -element field, and propose some extremal problems for intersecting families. These are $q$ -analogue of ErdÅs-Ko-R…

math.CO2025

A semidefinite programming approach to cross $2$ -intersecting families

Hajime Tanaka, Norihide Tokushige

Let $k \geq 2$ and $n \geq 3 (k - 1)$ . Let $F$ and $G$ be families of $k$ -element subsets of an $n$ -element set. Suppose that $∣ F \cap G ∣ \geq 2$ for all $F\in\mathcal…

math.CO2024

Burning Hamming graphs

Norihide Tokushige

The Hamming graph $H (n, q)$ is defined on the vertex set $[q]^{n}$ and two vertices are adjacent if and only if they differ in precisely one coordinate. Alon \cite{Alon} proved that t…

Burning numbers via eigenpolytopes -- Hamming graphs, Johnson graphs, and halved cubes

Alon's transmitting problem and multicolor Beck--Spencer Lemma

Extremal problems for intersecting families of subspaces with a measure

A semidefinite programming approach to cross 2-intersecting families

Burning Hamming graphs

A semidefinite programming approach to cross $2$ -intersecting families