id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
cord-190332-uovhtaxb	Eppstein, David	Tracking Paths in Planar Graphs	2019-08-15		.txt	text/plain	5676	401	77	On a high level, the proof of Lemma 6 is done by keeping a set of "active" trackers while reconstructing a planar embedding E of G: we start, as a base case, with any simple s − t path in E and iteratively add faces to it until it matches E. By Lemma 5, there is at least one entry-exit pair in E with respect to face C, so any tracking set must contain a tracker on some vertex of C. While there exist non-adjacent vertices u, v / ∈ {s, t} of degree 2 in a 4-cycle, place a tracker on either u or v and remove it and its edges from the graph. We show that Tracking can be solved in linear time when the input graph has bounded clique-width, by applying Courcelle's theorem [7, 8, 10 ], a powerful meta-theorem that establishes fixed-parameter tractability of any graph property that is expressible in monadic second order logic.	./cache/cord-190332-uovhtaxb.txt	./txt/cord-190332-uovhtaxb.txt