I am having a question in an Assignment at my college: How can i find the maximum number of pairs of node-disjoint-copies of 5-complete (sub-) graphes (K5) which are included in an 5-planarisable graph G ?
Hint: k-planarisable graphs is when we have S a subset of V (Vertexes Set of Graph G) where |S| = k and V - S = planar Graph I was trying to find out how many K5 in G through counting the number of the edges which the K5 should have AND the number of Edges for the G knowing that it is 5-planar (with at least 10 nodes to be able to have at least one pair of node-disjoint-copies of K5 knowing that the planar graph has maximally 3n-6 Edges (Euler theorem) where n is the number of nodes ). The solution should be done in using the Combinatoric formula, but i could't come along to a result.
Thank you so much in advance :)