Problem

Source: 2023 IRN-SGP-TWN Friendly Math Competition P4

Tags: graph theory, combinatorics



On a connected graph $G$, one may perform the following operations: choose a vertice $v$, and add a vertice $v'$ such that $v'$ is connected to $v$ and all of its neighbours choose a vertice $v$ with odd degree and delete it Show that for any connected graph $G$, we may perform a finite number of operations such that the resulting graph is a clique. Proposed by idonthaveanaopsaccount