Combinatorial and Discrete Geometry: Sheet H
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York 11451
web page: http://www.york.cuny.edu/~malk
The complement of a graph G is a graph with the same vertex set as G but whose edge set consists of those edges not in G. (The edges in G and its complement together form a complete graph on the number of vertices of G.
1. For each graph below draw the complement of the graph shown
2. If G is connected and has an Eulerian circuit, must its complement also have an Eulerian circuit? (If not, give an example which shows that this statement does not hold.)
If a statement is false as shown by an example, you can try to find an additional condition which might make the statement true.
3. If G is connected must the complement of G be connected? (If not, give an example which shows that this statement does not hold.)