Spanning Plane Subgraphs of 1‐Plane Graphs

ABSTRACT A graph drawn on the plane is called 1‐plane if each edge is crossed at most once by another edge. In this paper, we show that every 4‐edge‐connected 1‐plane graph has a connected spanning plane subgraph. We also show that there exist infinitely many 4‐connected 1‐plane graphs that have no 2‐connected spanning plane subgraphs. Moreover, we consider the condition of and such that every ‐connected 1‐plane graph has an ‐connected spanning plane subgraph.