初始点任意的摄动梯度投影法

Total Colouring of Highly Irregular Graph

利用梯度投影与罚函数相结合的技巧，将带不等式和等式约束的优化问题化成一个无约束问题，提出了初始点可任意的求解不等式、等式约束优化问题的摄动梯度投影算法；参数δｋ取不同的数还可以得到一类梯度投影算法，从而得出了在搜索方向和步长不精确条件下的梯度投影法，保证了在实际应用中更容易实现；在较弱条件下，证明了该算法的全局收敛性。

A proper k total colouring of a graph G is a colouring to its vertices and edges using k colours such that no two adjacent or incident elements (vertices or edges) of G may be assigned the same colour.The k is called total chromatic number of graph G if k is minimal.The symbol χ T(G) is used to denoted the chromatic number.We call a simple graph G a highly irregular graph if the degree of u′ is not equal to the degree of u″ for any u′,u″∈N(v) and for any vertex v of G ,where N(v) is the neighborhood of v .Let G be a highly irregular graph and Δ( G ) is its maximum degree.We show that if Δ( G )≥2,then χ T(G )=Δ( G )+1.A total colouring algorithm of G is also obtained.