Edge colorings of planar graphs

The research on edge coloring is mainly divided into two categories. One is to study the edge chromatic number of graphs, and the other is to study the conditions for the existence of subgraphs with certain coloring characteristics in edge colored graphs. This thesis studies the edge chromatic number under three generalizations of edge coloring (list edge coloring, signed edge coloring, and DP-edge coloring). The main results are as follows:
(1) We study the structure of signed critical graphs, obtain two adjacent lemmas
about signed critical graphs. We prove that the signed edge chromatic number of planar graphs with maximum degree at least eight or planar graphs with maximum degree at least six and any 6-cycle contains at most one chord is its maximum degree.
(2) We prove that the list edge chromatic number of planar graphs with maximum degree at least six and any 7-cycle contains no chord is not more that its maximum degree plus one.
(3) We prove that the DP-edge chromatic number of planar graph with maximum degree at least seven and contains no 4-cycle or planar graph with maximum
degree at least eight and contains no 3-cycle is its maximum degree; the edge DP chromatic number of planar graph with maximum degree at least nine is
not more that its maximum degree plus one.