Study On1-planar Graphs Of Some List Edge Coloring

One of the main subjects of graph theory is coloring of graphs. In this paper, we have some considerations concerning1-planar graphs on list edge and list total coloring of simple graphs.A graph G is1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge.The mapping L is said to be a total assignment for the graph G if it assigns a list L(x)of possible colors to each element x∈V(?) E. If G has a total coloring c such that c(x)∈L(x) for all x∈V(?) E, then we say that G is total colorable, or G is total-L-colorable. A graph G is k-total-choosable if G has a proper L-total-coloring for every total assignment L satisfying|L(x)≥k|for all elements x∈V(?)E. The list total chromatic number or tatal choosability of G, denoted xl"(G), is the smallest integer k such that G is k-total-choosal. The list edge chromatic number (or edge choosability)xl’(G) are defined similarly.In this thesis, basing on the construction and properties of graph, using the methods of discharging. we have researched a lower bound for the size of list edge and list total coloring of1-planar graphs and obtain some result.In chapter1, we introduced the history, some basic definitions of graph theory and the research background of this paper.In chapter2,we main prove the results about list edge and list total coloring of adjacent triangle-free Of1-planar graphs:1.The list edge chromatic numberxl’(G)=Δ and the list total chromatic number xl’’(G)=Δ+1if Δ≥17.2.The list edge chromatic number xl’(G)=Δ+1and the list total chromatic number xl’’(G)=Δ+2if Δ≥13.In chapter3,we main prove the results about list edge and list total coloring of adjacent4-cycle free of1-planar graphs:1.The list edge chromatic numberxl’(G)=Δ and the list total chromatic number xl’’(G)=Δ+1if Δ≥19.2.The list edge chromatic numberxl’’(G)=Δ+1and the list total chromatic number xl’’(G)=Δ+2if Δ≥13.The chapter4,we mainly summarize the conclusions briefly and give the prospects.