Stijn Cambie

collaborators

7 papers

math.CO2026

Solution of ErdÅs problem $#443$

Stijn Cambie

We prove that the size $# {k (m - k) : 1 \leq k \leq m /2} \cap {l (n - l) : 1 \leq l \leq n /2}$ is $(mn)^{o (1)}$ , but can be arbitrarily large. This resolves ErdÅs problem $#443$ .

math.CO2026

On the order-diameter ratio of girth-diameter cages

Stijn Cambie, Jan Goedgebeur, Jorik Jooken +1

For integers $k, g, d$ , a $(k; g, d)$ -cage (or simply girth-diameter cage) is a smallest $k$ -regular graph of girth $g$ and diameter $d$ (if it exists). The order of a $(k; g, d)$ -cage i…

math.CO2026

A general bound on $R (C_{k}, H)$

Stijn Cambie, Andrea Freschi

In this paper, we prove that for every $k$ and every graph $H$ with $m$ edges and no isolated vertices, the Ramsey number $R (C_{k}, H)$ is at most $(k - 1) m + 1 \leq k m$ . This settles a pro…

math.CO2026

Benjamini-Schramm convergence and subtrees of trees

Stijn Cambie, Stephan Wagner, Ruoyu Wang

In this paper, we study the asymptotic behaviour of the number of subtrees and the subtree density for a sequence of trees that converges in the Benjamini-Schramm sense. Benjamini-…

math.CO2026

Maximum ratio of (graph) irregularities

Stijn Cambie, Jionghua Chang

We estimate the maximum ratio between the $I ¨ _{t}$ - and $I ¨ $ -irregularity for graphs and trees of order $n$ , which are respectively bounded by $I^ (n^{5/2})$ and $n - 2$ . This answers a…

math.CO2026

On the maximum product of distances of diameter $2$ point sets

Stijn Cambie, Arne Decadt, Yanni Dong +2

We consider a problem posed by ErdÅs, Herzog and Piranian on the maximum product of distances of a point set of order $n$ with a given diameter. We prove that it is sufficient to…

Solution of ErdÅs problem #443

On the order-diameter ratio of girth-diameter cages

A general bound on R(Ck​,H)

Benjamini-Schramm convergence and subtrees of trees

Maximum ratio of (graph) irregularities

On the maximum product of distances of diameter 2 point sets

Solution of ErdÅs problem $#443$

A general bound on $R (C_{k}, H)$

On the maximum product of distances of diameter $2$ point sets