Study on two colours painting patterns using dual structures of graph theories

Abstract

As a building finishing pattern(B.F.P.), we use so many 2-colour painting pattern(2-C.P.P.), such as check, lattice, stripe and dots pattern. But when we analize 2-C.P.P., we must aware two different situations, one is figures on the free plane, another on the flamed plane like a B.F.P.. Normaly we analize 2-C.P.P. on the free plane using dual structure of graph theory. In case of 2-C.P.P. on flamed plane, we must additionaly consider dual structure of 3-C.P.P.. This report discussed the dual structure's condition which lead to 2-C.P.P. both on the free plane and on flamed plane, using linear graph, plane graph, and cubic graph.