Adaptive majority problems for restricted query graphs and for weighted sets

Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color occurs on more than half is called majority (if it exists), and any vertex this . We study problem finding (or show none if we can query edges to learn whether their endpoints have same or different colors. Denote least number queries needed worst case by m ( ) It was shown Saks Werman K n = − b , where 1’s binary representation In paper initiate for general graphs. obvious bounds connected ≤ 1 tree T even odd vertices, 65 2 Our proof uses results about weighted version which may be independent interest. also exhibit sequence graphs such has O vertices.