In this paper, the chromatic sum functions of rooted biloopless nonsepavable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From...In this paper, the chromatic sum functions of rooted biloopless nonsepavable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived.展开更多
Let G be a k（k ≤ 2）-edge connected simple graph with minimal degree ≥ 3 and girth g, r = [g-1/2]. For any edge uv ∈ E（G）, if dG（u） ＋ dG（v） 〉2v（G） - 2（k ＋ 1）（9 - 2r）/（k ＋ 1）（2r - 1）（g - 2r）...Let G be a k（k ≤ 2）-edge connected simple graph with minimal degree ≥ 3 and girth g, r = [g-1/2]. For any edge uv ∈ E（G）, if dG（u） ＋ dG（v） 〉2v（G） - 2（k ＋ 1）（9 - 2r）/（k ＋ 1）（2r - 1）（g - 2r）＋ 2（g - 2r - 1）,then G is up-embeddable. Furthermore, similar results for 3-edge connected simple graphs are also obtained.展开更多
基金Supported by the National Natural Science Foundation of China (No. 10771225 10871021+1 种基金 71071016) Fundamental Research Funds for the Central Universities
文摘In this paper, the chromatic sum functions of rooted biloopless nonsepavable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived.
基金Supported by National Natural Science Foundation of China(No.11301171)Hunan youth backbone teachers training Program(H21308)+1 种基金Tianyuan Fund for Mathematics(No.11226284)Hunan Province Natural Science Fund Projects(No.13JJ4079,14JJ7047)
文摘Let G be a k（k ≤ 2）-edge connected simple graph with minimal degree ≥ 3 and girth g, r = [g-1/2]. For any edge uv ∈ E（G）, if dG（u） ＋ dG（v） 〉2v（G） - 2（k ＋ 1）（9 - 2r）/（k ＋ 1）（2r - 1）（g - 2r）＋ 2（g - 2r - 1）,then G is up-embeddable. Furthermore, similar results for 3-edge connected simple graphs are also obtained.
