发表机构
Macao Polytechnic University（澳门理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对良序$k$-退化图，提出首个生成、排名与反排名循环枢轴格雷码的简单算法，相邻图通过单边增删或枢转区分，生成达到常数摊还时间，排名与反排名均为$O(n^2)$时间与空间。
AI 中文摘要
若图$G$的顶点存在一个排序$v_1, v_2, \dots, v_n$，使得每个顶点$v_i$在$G$中至多有$k$个满足$j < i$的邻居$v_j$，则称$G$为$k$-退化图。良序$k$-退化图是顶点集为$\{1, 2, \dots, n\}$的标号图，其中每个顶点$i$在$1, 2, \dots, i-1$中至多有$k$个邻居。我们首次提出简单的算法，用于生成、排名和反排名良序$k$-退化图的循环枢轴格雷码，其中相邻图通过添加、移除或枢转单条边而不同。我们的算法以每个图常数摊还时间生成每个良序$k$-退化图，使用$O(n^2)$空间，而排名和反排名需要$O(n^2)$时间和$O(n^2)$空间。
英文摘要
A graph $G$ is $k$-degenerate if there exists an ordering $v_1, v_2, \dots, v_n$ of its vertices such that each vertex $v_i$ has at most $k$ neighbors $v_j$ in $G$ with $j < i$. A well-ordered $k$-degenerate graph is a labeled graph on the vertex set $\{1, 2, \dots, n\}$ in which every vertex $i$ has at most $k$ neighbors among $1, 2, \dots, i-1$. We present the first simple algorithms that generate, rank, and unrank cyclic pivot Gray codes for well-ordered $k$-degenerate graphs, where consecutive graphs differ by the addition, removal, or pivoting of a single edge. Our algorithm generates each well-ordered $k$-degenerate graph in constant amortized time per graph, using $O(n^2)$ space, while ranking and unranking take $O(n^2)$ time and $O(n^2)$ space.
Comments38 pages, 4 figures
