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Improper colouring of graphs with no odd clique minor

  • Dong Yeap Kang (a1) and Sang-Il Oum (a1) (a2)


As a strengthening of Hadwiger’s conjecture, Gerards and Seymour conjectured that every graph with no odd Kt minor is (t − 1)-colourable. We prove two weaker variants of this conjecture. Firstly, we show that for each t ⩾ 2, every graph with no odd Kt minor has a partition of its vertex set into 6t − 9 sets V1, …, V6t−9 such that each Vi induces a subgraph of bounded maximum degree. Secondly, we prove that for each t ⩾ 2, every graph with no odd Kt minor has a partition of its vertex set into 10t −13 sets V1,…, V10t−13 such that each Vi induces a subgraph with components of bounded size. The second theorem improves a result of Kawarabayashi (2008), which states that the vertex set can be partitioned into 496t such sets.


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The first author was supported by a TJ Park Science Fellowship of POSCO TJ Park Foundation.

Supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (no. NRF-2017R1A2B4005020).



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Improper colouring of graphs with no odd clique minor

  • Dong Yeap Kang (a1) and Sang-Il Oum (a1) (a2)


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