曲面上无三角形图的三色染色 IV：4-临界图的面大小界定
组合数学
2020-08-05 v4
摘要
设 G 为一个嵌入在亏格为 g 的曲面上的 4-临界图，包含 t 个三角形。设 c 为 G 中不界定 2-胞腔面的 4-圈的数量。我们证明了 G 中长度 (5) 的面的长度之和至多是关于 g+t+c-1 的线性函数。
引用
@article{arxiv.1404.6356,
title = {Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes of 4-critical graphs},
author = {Zdenek Dvorak and Daniel Kral and Robin Thomas},
journal= {arXiv preprint arXiv:1404.6356},
year = {2020}
}
备注
28 pages, 1 figure v2: Several changes necessitated by further papers in the series included. Fixed an error: excluding only separating non-contractible 4-cycles is not enough. v3: Added a result on number of vertices needed to remove to make a graph 3-colorable v4: Updated for reviewer comments