2022/04/14 by Dourado, Mitre C., Grippo, Luciano N., Valencia-Pabon, Mario
#05C85 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.2.2
paper · doi:10.48550/arxiv.2204.06842
Let G be a graph having a vertex v such that H = G - v is a trivially perfect graph. We give a polynomial-time algorithm for the problem of deciding whether it is possible to add at most k edges to G to obtain a trivially perfect graph. This is a slight variation of the well-studied \sc Edge Completion, also known as \sc Minimum Fill-In, problem. We also show that if H is a chordal graph, then the problem of deciding whether it is possible to add at most k edges to G to obtain a chordal graph is \NP-complete.