Some Sufficient Conditions For A Planar Graph To Has A Strictly F-degenerate Transvereal

The graph coloring problem is an important branch in graph theory.The subject of graph theory originated from the famous K?nigsberg Seven Bridges problem.The vertex coloring problem of graph theory is a hot topic and it originated from ”four-color conjecture” proposed by Guthrie in 1852.With the development of graph theory,Vizing proposed the list coloring,which is a generalization of the proper coloring.In 2015,Dvo?ák and Postle proposed the DPcoloring,which is a generalization of the list coloring.Before and during this period,some other colorings were proposed successively,such as the vertex arboricity and the degenerate problems,etc.In 2018,T.Wang proposed the problem of strictly f-degenerate transversal of graphs(SFDT for short),which is a generalization of all above colorings and this has a great research significance.By studying the related papers of vertex arboricity,DP-coloring and degenerate problems,we can better study the SFDT problem of graphs.Whether there has an SFDT in G is a problem worthy studying.In this paper,it is divided into five chapters.The first two chapters are about some basic terms and definitions,as well as some related conclusions.In chapter three,we give a result on strictly f-degenerate transversal of toroidal graphs without small subgraphs,which improves many known results on(list)vertex arboricity and DP-coloring.In chapter four,we present a result on strictly f-degenerate transversal of planar graphs without intersecting 5-cycles,which improves that every planar graph without intersecting 5-cycles is DP-4-colorable.Chapter five is the summary and prospect.