J. G. van der Pol

activity

20122022

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Showing 2021Show all

3 papers · 1 filter

math.CO2021

Tuza's conjecture for binary geometries

Kazuhiro Nomoto, Jorn van der Pol

Tuza (A conjecture, in Proceedings of the Colloquia Mathematica Societatis Janos Bolyai, 1981) conjectured that $τ (G) \leq 2 ν (G)$ for all graphs $G$ , where $τ (G)$ is the minimum siz…

math.CO2021

Almost every matroid has an $M (K_{4})$ - or a $W^{3}$ -minor

Jorn van der Pol

We show that almost every matroid contains the rank-3 whirl $W^{3}$ or the complete-graphic matroid $M (K_{4})$ as a minor.

math.CO2021

Enumeration of extensions of the cycle matroid of a complete graph

Peter Nelson, Shayla Redlin, Jorn van der Pol

We prove that the number of single element extensions of $M (K_{n + 1})$ is $2^{(n /2 n) (1 + o (1))}$ . This is done using a characterization of extensions as "linear subclasses".

Tuza's conjecture for binary geometries

Almost every matroid has an M(K4​)- or a W3-minor

Enumeration of extensions of the cycle matroid of a complete graph

Almost every matroid has an $M (K_{4})$ - or a $W^{3}$ -minor