完全三部圖的邊覆蓋染色.pdf

1、河北工業(yè)大學碩士學位論文完全三部圖的邊覆蓋染色姓名：王猛申請學位級別：碩士專業(yè)：應用數學指導教師：徐常青20091201??nÜã?>CX/ÚEDGE COVERING COLORINGS OFCOMPLETE TRIPARTITE GRAPHSABSTRACTLet ?(?, ?) be a simple graph with vertex set ? (?) and edge set ?(?).?

2、 is a mapping from ?(?) to a color set {1, 2, ..., ?}, and ? is called a ?-edge-coloring of ?, if ?: ? → {1, 2, ..., ?}. Let ??1 ? (?) denote the numberof edges of ? incident with vertex ? receiving color ? by the colori

3、ng ?. ?is called a ?-edge cover-coloring of ? if ??1 ? (?) ≥ 1 for each ? ∈ ? , and? ∈ {1, 2, ..., ?}. Let ?′ ?(?) be the maximum positive integer ? for which anedge cover-coloring with ?- colors of ? exists. Then ?′ ?(?

4、) is called the edgecover chromatic index of ?. It is known that ??1 ≤ ?′ ?(?) ≤ ?. ? is a graphof ?? class if ?′ ?(?) = ?, otherwise ? is a graph of ??? class. It is easyto prove that the problem of deciding whether a g

5、iven graph is of ?? classor ??? class is ??-complete. In this paper§ we consider the classificationof complete tripartite graphs based on the edge cover chromatic index andobtain a necessary and sufficient condition