1 DISCRETE MATHEMATICS 2
Final Exam Sample 2016 1. Show that χ0(T ) = ∆(T ) for every tree T .
2. Show that if G is a connected bipartite planar graph then G∗ is eulerian.
3. Let G be a graph with at least 5 vertices. Show that, if for every two vertices u, v ∈ V (G) there exists in G a Hamilton path with ends u and v, then G is 3-connected.
4. Show that
e(G) ≥ χ(G) 2
!
for every connected graph G with at least one edge.
5. Construction of optimal spanning trees - Kruskal Algorithm (with proof of correctness).
For each task maximally 12 points can be obtained
