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arXiv · 1810.12873

The structure of graphs with no K_{3,3} immersion

Matt DeVos·Mahdieh Malekian
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Abstract

The Kuratowski-Wagner Theorem asserts that a graph is planar if and only if it does not have either $K_{3,3}$ or $K_5$ as a minor. Using this Wagner obtained a precise description of all graphs with no $K_{3,3}$ minor and all graphs with no $K_5$ minor. Similar results have been achieved for the class of graphs with no $H$-minor for a number of small graphs $H$. In this paper we give a precise structure theorem for graphs which do not contain $K_{3,3}$ as an immersion. This strengthens an earlier theorem of Giannopoulou, Kami\'{n}ski, and Thilikos that gives a rough description of the class of graphs with no $K_{3,3}$ or $K_5$ immersion.

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Matt DeVos, Mahdieh Malekian. 2018-10-30. The structure of graphs with no K_{3,3} immersion. https://arxiv.org/abs/1810.12873

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