2018/11/19 by Gabriela Araujo‐Pardo, Araujo-Pardo, Gabriela, Fidel Barrera-Cruz +3
Computer Science · Engineering · #05C1 #05C35 #Advanced Graph Theory Research #Advanced Materials and Mechanics #Combinatorics (math.CO) #FOS: Mathematics #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1811.07449
openalex publication_date 2018/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Cage Problem for regular and biregular planar graphs. A (k,g)-graph is a k-regular graph with girth g. A (k,g)-cage is a (k,g)-graph of minimum order. It is not difficult to conclude that the regular planar cages are the Platonic Solids. A (\r,m\;g)-graph is a graph of girth g whose vertices have degrees r and m. A (\r,m\;g)-cage is a (\r,m\;g)-graph of minimum order. In this case we determine the triplets of values (\r,m\;g) for which there exist planar (\r,m\;g)--graphs, for all those values we construct examples. Furthermore, for many triplets (\r,m\;g) we build the (\r,m\;g)-cages.