Abstract
In this chapter we address the question of which graphs are such that their line graphs can be drawn in the plane in such a way that none of their edges cross. It turns out that there are two criteria for this, one involving forbidden subgraphs, the other involving degrees and connectivity properties of individual vertices. After reviewing briefly some of the background of planar graphs, these criteria are proved along with some related results. In particular, we prove which line graphs can have drawings in which all of the vertices are on the unbounded region. We follow this with an investigation into graphs for which the line graph can be drawn in the plane with just one crossing of edges. The chapter concludes with results on the potential behavior of the iterated line graphs in the plane.
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Beineke, L.W., Bagga, J.S. (2021). Planarity of Line Graphs. In: Line Graphs and Line Digraphs. Developments in Mathematics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-030-81386-4_5
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DOI: https://doi.org/10.1007/978-3-030-81386-4_5
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