Author

S. Norin

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Preprint Aug 2026

Two Relaxations of the Dominating Hadwiger's Conjecture

Illingworth and Wood recently proposed the Dominating Hadwiger's Conjecture, a strengthening of Hadwiger's Conjecture which asserts that every graph with no dominating $K_t$-model is $(t-1)$-colorable. We prove two relaxations of this conjecture. First, we show that every graph with average degree $Ct (\log t)^2$ conta...

António Girão, S. Norin, Youri Tamitegama et al. · 0 citations

Preprint Sep 2026

Every graph with no $K_7^=$ minor is 6-colorable

The first open case of Hadwiger's conjecture states that every $K_7$-minor-free graph is 6-colorable. We prove that this is the case for $K_7^=$-minor-free graphs, where $K_7^=$ denotes the graph obtained from $K_7$ by deleting two independent edges. The proof is based on an independently interesting density result: Ev...

Zdeněk Dvořák, S. Norin, Neil Rahman · 0 citations

Jul 2026

Nerve-type and invariance theorems for asymptotic dimension

Asymptotic dimension of metric spaces is a large-scale analog of covering dimension of topological spaces. An intersection graph of a family of sets is the graph whose vertices are the members of the family and whose edges correspond to pairs of members with non-empty intersection. Our first main result connects the as...

Chun-Hung Liu, S. Norin · arXiv.org · 0 citations