Abstract
Prior work on contact representations of planar graphs deals with undirected graphs only. We introduce a notion of point-side contact representations for directed planar graphs. We show every outerplanar digraph of out-degree at most three to enjoy a point-side triangle contact representation. The result is generalized to outerplanar digraphs of out-degree at most n, which are shown to have convex n-gon (i.e., n-sided polygon) point-side contact representations. Our result is tight is the sense that there exists a 2-outerplanar digraph that does not have a point-side triangle contact representation. For maximal outerplanar digraphs of out-degree at most three, an efficient constructive procedure is designed to yield their point-side triangle contact representations. For general planar digraphs of degree d, they are shown to admit 2d-gon point-side contact representations.
H.-C. Yen—Research supported in part by Ministry of Science and Technology, Taiwan, under grant MOST 106-2221-E-002-036-MY3.
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Chan, CH., Yen, HC. (2018). On Contact Representations of Directed Planar Graphs. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_19
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