Total Coloring And List Total Coloring For Planar Graphs

This dissertation studies total coloring and list total coloring for planar graphs. By discharging, It is proved that(1) if G is a C4-free plane graph of A(G)= 6 ,then XT(G)< 8.(2) if G is a plane graph with maximum degree 9 and without 4-cycles, then xt(G)=10.(3) if G is a plane graph with maximum degree 11 and without adjacent triangles ,then chT(G) = XT((G)=12.These results support the Total Coloring Conjecture and the List Total Coloring Conjecture further.