论文标题
定期棋盘表的表征功能区图
Characterization of regular checkerboard colourable twisted duals of ribbon graphs
论文作者
论文摘要
细胞嵌入图的几何双重偶是图理论中的一个基本概念，并且也出现在数学的许多其他分支中。部分双重二元是一个必不可少的概括，可以通过仅相对于细胞嵌入图的边缘的子集形成几何偶来获得。扭曲的双重是通过结合部分石化的进一步概括。在本文中，给定一个功能区图$ g $，我们首先使用跨度的Quasi-Tree及其相关的较短标记箭头序列集来表征色带图$ G $的常规部分双偶。然后，我们通过使用跨越树和相关的伴随概念来表征任何Eulerian功能区图形的棋盘表演局部皮质。最后，我们对功能区图的所有常规核心板的扭曲双重双重的双重表征进行了完整的表征，该曲线解决了Ellis-Monaghan和Moffatt提出的问题[T. T.是。数学。 Soc。，364（3）（2012），1529-1569]。
The geometric dual of a cellularly embedded graph is a fundamental concept in graph theory and also appears in many other branches of mathematics. The partial dual is an essential generalization which can be obtained by forming the geometric dual with respect to only a subset of edges of a cellularly embedded graph. The twisted dual is a further generalization by combining the partial Petrial. Given a ribbon graph $G$, in this paper, we first characterize regular partial duals of the ribbon graph $G$ by using spanning quasi-tree and its related shorter marking arrow sequence set. Then we characterize checkerboard colourable partial Petrials for any Eulerian ribbon graph by using spanning trees and a related notion of adjoint set. Finally we give a complete characterization of all regular checkerboard colourable twisted duals of a ribbon graph, which solve a problem raised by Ellis-Monaghan and Moffatt [T. Am. Math. Soc., 364(3) (2012), 1529-1569].
