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math.CO2022★ 1 cited
Non-Crossing Shortest Paths are Covered with Exactly Four Forests
Lorenzo Balzotti
Given a set of paths we define the \emph{Path Covering with Forest Number} of } (PCFN()) as the minimum size of a set of forests satisfying that every path in is…
math.CO2022
Two New Characterizations of Path Graphs
Nicola Apollonio, Lorenzo Balzotti
Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection Graphs of Paths i…