The Linear Arboricity And Linear 2-arboricity Of Planar Graphs

Arboricity of graphs is theory about coloring of graphs. The theory of coloring have various research on scheduling problem, divisionoflabour problem and transportation problem. The research of coloring of graphs begin with vertex coloring as four-colour problem. After that research of edge coloring appear. Vertex coloring of graphs G is the partition of V(G) with independent set. Edge coloring of graphs G is the partition of E(G) with independent set. A problem has been put forward: whether V(G) and E(G) can be partition into other form like tree? So, the theory of arboricity of graph emerge.1970å¹´, Harary advance the notation of arboricity of graph.1980å¹´, Akiyama,Exooå'ŒHarary make a conjecture:For any regular graph G,Then, the well-known Linear Arboricity Conjecture is started as follows:For any simple graph G,Based on the above research backgrounds, this paper revolve about the linear arboricity and the linear 2-arboricity of graph. This paper is divided into four chapters:In first chapter,we give some related research backgrounds and some known results. In the meantime, we also give a brief introduction about the basic concepts, terminologies and symbols which will be used in this paper. In the second chapter, we mainly study the linear 2-arboricity of graph and introduct some results of linear 2-arboricity of graphs.The thied chapter is devoted to study the linear arboricity of graphs without chordal-k-cycles.In the fourth chapter, we study the linear 2-arboricity of graph without chordal-5-cycles. Main results are described as follows:If G is a graph without chordal-5-cycles, then...