Zdenek Dvorak, Daniel Kral, Robin Thomas
Published 2014-04-25, updated 2015-01-18Version 2
Let G be a 4-critical graph with t triangles, embedded in a surface of genus g. Let c be the number of 4-cycles in G that do not bound a 2-cell face. We prove that the sum of lengths of (>=5)-faces of G is at most linear in g+t+c-1.
Comments: 28 pages, 1 figure Several changes necessitated by further papers in the series included. Fixed an error: excluding only separating non-contractible 4-cycles is not enough. arXiv admin note: substantial text overlap with arXiv:1402.4710
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