someone strange birthday present Ivan it hedgehog connect undirected graph vertex degree 3 center vertex degree 1 Ivan think hedgehog boring decide kmultihedgehogLet define kmultihedgehog follow 1multihedgehog hedgehog vertex degree 3 vertex degree 1 for k ge 2 kmultihedgehog k1multihedgehog follow change vertex v degree 1 let u neighbor remove vertex v create new hedgehog center vertex w connect vertex u w edge new hedgehog differ initial gift Thereby kmultihedgehog tree Ivan kmultihedgehog sure mistake that ask check tree kmultihedgehog