Counting paths, cycles, and blow‐ups in planar graphs
Christopher Cox, Ryan R. Martin · Journal of Graph Theory · 2022
Abstract For a planar graph , let denote the maximum number of copies of in an ‐vertex planar graph. In this paper, we prove that , , , and , where is the 1‐subdivision of . In addition, we obtain significantly improved upper bounds on and for . For a wide class of graphs , the key technique developed in this paper allows us to bound in terms of an optimization problem over weighted graphs.