2019/04/26 by Kostochka, Alexandr V., Nahvi, Mina, West, Douglas B. +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1904.11901
The k-deck of a graph is the multiset of its subgraphs induced by k vertices. A graph or graph property is l-reconstructible if it is determined by the deck of subgraphs obtained by deleting l vertices. We show that the degree list of an n-vertex graph is 3-reconstructible when n≥7, and the threshold on n is sharp. Using this result, we show that when n≥7 the (n-3)-deck also determines whether an n-vertex graph is connected; this is also sharp. These results extend the results of Chernyak and Manvel, respectively, that the degree list and connectedness are 2-reconstructible when n≥6, which are also sharp.