Two remarks about multicurve graphs on infinite-type surfaces

Abstract

After Fossas-Parlier [9], we consider two graphs G0(S) and G∞(S), constructed from multicurves on connected, orientable surfaces of infinite-type.Our first result asserts that G∞(S) has finite diameter, which extends a result of Fossas-Parlier [9]. Next, we prove that the group of (labelpreserving) automorphisms of G0(S) is the extended mapping class group of S, which may be regarded as an infinite-type analog of a theorem of Margalit [12] about pants complexes.