Obstructions for two-vertex alternating embeddings of graphs in surfaces

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• 作者：Bojan Mohar¹ ; Petr &Scaron ; koda ^{pskoda@sfu.ca" class="auth_mail" title="E-mail the corresponding author}
• 刊名：European Journal of Combinatorics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：59
• 期：Complete
• 页码：96-113
• 全文大小：532 K

文摘

A class of graphs that lies strictly between the classes of graphs of genus (at most) k−1$k-1$ and 0329f2" title="Click to view the MathML source">k$k$ is studied. For a fixed orientable surface 034b87b164106daae36597ec38213a14" title="Click to view the MathML source">S_k${\mathbb{S}}_k$ of genus 0329f2" title="Click to view the MathML source">k$k$, let ${\mathcal{A}}_{xy}^k$ be the minor-closed class of graphs with terminals 3e3d87" title="Click to view the MathML source">x$x$ and e20c43011bd1b2ca6791a0ccac5f" title="Click to view the MathML source">y$y$ that either embed into S_k−1${\mathbb{S}}_{k-1}$ or admit an embedding Π$\Pi$ into 034b87b164106daae36597ec38213a14" title="Click to view the MathML source">S_k${\mathbb{S}}_k$ such that there is a Π$\Pi$-face where 3e3d87" title="Click to view the MathML source">x$x$ and e20c43011bd1b2ca6791a0ccac5f" title="Click to view the MathML source">y$y$ appear twice in the alternating order. In this paper, the obstructions for the classes ${\mathcal{A}}_{xy}^k$ are studied. In particular, the complete list of obstructions for ${\mathcal{A}}_{xy}^1$ is presented.