发表机构
American University of the Middle East（中东美国大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
介绍无分裂电缆术语和电缆博弈，一种顺序图构造语言，证明顺序无分裂宽度至少是线性秩宽两倍，给出特定条件下线性秩宽最多为1的精确刻画，还对树等情况进行了研究并提出猜想。
AI 中文摘要
我们引入无分裂电缆项和电缆博弈，一种顺序图构造语言，其活动电缆在当前割上强制实现均匀的GF(2)行行为。宽度为w的每个博弈给出一个出生顺序布局，其割秩至多为w向下取整的一半，所以顺序无分裂宽度至少是线性秩宽的两倍。在第一个非平凡层次，我们证明了一个精确刻画：一个至少有两个顶点的连通图的线性秩宽至多为1，当且仅当它允许一个流，等价地，一个宽度至多为4的单出生博弈。我们表明无限制项宽度和顺序宽度在树上无界地不同，在网格图上校准构造，并提出一个将顺序无分裂宽度与线性秩宽相关的仿射上界猜想。对于秩为2的情况，我们证明了一个双累加器调度准则，在自然的未来均匀性假设下产生宽度为6的博弈。
英文摘要
We introduce split-free cable expressions and their sequential restriction. Live cables are vertex blocks that future operations cannot split. The main result identifies sequential split-free cable width, up to an additive two, with active neighborhood-width, the minimum number of distinct nonzero future-neighborhood classes across a linear layout. The lower bound extracts such a layout from every cable play and includes a parity argument for prefixes inside a birth group. The upper bound compiles any active-neighborhood layout into a singleton-birth play. This gives an exponential upper bound and a linear lower bound in terms of linear rank-width. We prove that the complement of the seven-vertex cycle has linear rank-width two and sequential cable width exactly eight. This disproves the proposed affine upper estimate already at rank two. We also prove an unbounded separation between branching expression width and sequential width on trees.
Comments14 pages. Metadata corrected to match the revised manuscript
