发表机构
Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对AT-free图、弦图和凸二分图，分别提出基于星冲突图、团树分解和边界索引的最大边开打包算法，时间复杂度分别为$O(n^2+m^4)$、$O(n^4)$和$O(n^4)$，并扩展了双凸二分图的结果。
AI 中文摘要
边开打包是一组边，其端点诱导出星的并集。我们研究在AT-free图、弦图和凸二分图中寻找最大边开打包的问题。对于AT-free图，我们使用由Das和Santra引入的有向星冲突图$A_G$，其中$\rho_e^o(G)=\alpha(A_G)$，并证明当$G$为AT-free时，$A_G$也是AT-free。因此，已知的AT-free图最大独立集算法可导出最大边开打包的$O(n^2+m^4)$时间算法，其中$n$和$m$分别表示$G$的顶点数和边数。对于弦图，我们利用边开打包的端点集与每个团相交至多两个顶点的结构事实，在由团树导出的良好树分解上开发了$O(n^4)$时间动态规划算法。最后，对于凸二分图，我们基于两个分隔连续星分量的边界索引，获得了$O(n^4)$时间动态规划算法。该结果扩展了先前针对双凸二分图的算法，并特别为该类提供了改进的显式运行时间界。
英文摘要
An edge open packing is a set of edges whose endpoints induce a disjoint union of stars. We study the problem of finding a maximum edge open packing in AT-free, chordal, and convex bipartite graphs. For AT-free graphs, we use the oriented star-conflict graph $A_G$, introduced by Das and Santra, for which $ρ_e^o(G)=α(A_G)$, and prove that $A_G$ is AT-free whenever $G$ is AT-free. Consequently, a known maximum independent set algorithm for AT-free graphs yields an $O(n^2+m^4)$-time algorithm for Maximum Edge Open Packing, where $n$ and $m$ denote the numbers of vertices and edges of $G$, respectively. For chordal graphs, we develop an $O(n^4)$-time dynamic programming algorithm over a nice tree decomposition derived from a clique tree, exploiting the structural fact that the endpoint set of an edge open packing intersects every clique in at most two vertices. Finally, for convex bipartite graphs, we obtain an $O(n^4)$-time dynamic programming algorithm based on two boundary indices that separate consecutive star components. This result extends the previously known algorithm for biconvex bipartite graphs and, in particular, provides an improved explicit running-time bound for that class.
