MathDB
Self-intersecting graph

Source: Iranian National Olympiad (3rd Round) 2008

September 20, 2008
combinatorics proposedcombinatorics

Problem Statement

A graph is called a self-intersecting graph if it is isomorphic to a graph whose every edge is a segment and every two edges intersect. Notice that no edge contains a vertex except its two endings. a) Find all n n's for which the cycle of length n n is self-intersecting. b) Prove that in a self-intersecting graph E(G)V(G) |E(G)|\leq|V(G)|. c) Find all self-intersecting graphs. http://i35.tinypic.com/x43s5u.png