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arXiv · 2610.06482

Deciding lettericity is NP-complete, even for four-colorable comparability graphs

Vincent Vatter
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Abstract

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.

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Vincent Vatter. 2026-10-05. Deciding lettericity is NP-complete, even for four-colorable comparability graphs. https://arxiv.org/abs/2610.06482

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