Vertex Reducible Total Coloring Algorithm for Random Graphs
Wang Li, Jingwen Li · 2023
For any undirected connected graph G(V, E), if there exists a surjection f: V(G) ∪ E(G) → {1, 2, ⋯ , k}, where k is a positive integer and the maximum is the number of points plus the number of edges such that the set of colors of all vertices of the same degree in the graph is the same, then the mapping relation f is called Vertex Reducible Total Coloring (VRTC) of the graph G, and the vertex reducible total chromatic number of the graph G is the maximum value k obtained. Aiming at the realistic problems that can be solved by the vertex reducible total coloring model, a new VRTC algorithm is designed with the traditional intelligent algorithm idea. The algorithm searches for the vertex reducible total chromatic number of random graphs within a finite number of points by means of continuous function, balance function, and adjustment function in an iterative, merit-seeking manner. By analyzing the result set and summarizing the coloring laws, several theorems are obtained.