发表机构
University of Florida（佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明判定图的lettericity至多为k是NP完全的，即使对四色可比图也成立，通过将二部图归约到其关联图的膨胀图，并利用边划分路径的NP完全性。
AI 中文摘要
我们证明，判定一个图的lettericity是否至多为k是NP完全的，即使对于四色可比图也是如此。我们的归约将二部图G映射到由其关联图通过将每个顶点膨胀为一个团或三个顶点的独立集而得到的图。该图的lettericity由G的顶点数和边数以及G中四条顶点上的边不相交路径的最大数量决定。Teypaz和Rapine证明了判定二部图的边是否可以被划分为四条顶点上的路径是NP完全的。
英文摘要
We prove that deciding whether a graph has lettericity at most k is NP-complete, even for four-colorable comparability graphs. Our reduction maps a bipartite graph G to the graph obtained from its incidence graph by inflating each vertex by a clique or an independent set of three vertices. The lettericity of this graph is determined by the numbers of vertices and edges of G and the greatest number of edge-disjoint paths on four vertices in G. Teypaz and Rapine showed that deciding whether the edges of a bipartite graph can be partitioned into paths on four vertices is NP-complete.
