【摘要】：令G是一個(gè)有限圖,H是G的一個(gè)子圖.若V(H)=V(G),則稱H為G的生成子圖.圖G的一個(gè)λ重F-因子,記為S_λ(F,G),是G的一個(gè)生成子圖且可分拆為若干與F同構(gòu)的子圖(稱為F-區(qū)組)的并,使得V(G)中的每一個(gè)頂點(diǎn)恰出現(xiàn)在λ個(gè)F-區(qū)組中.一個(gè)圖G的λ重F-因子大集,記為L(zhǎng)S_λ(F,G),是G中所有與F同構(gòu)的子圖的一個(gè)分拆{B_i},使得每個(gè)B_i均構(gòu)成一個(gè)S_λ(F,G).當(dāng)λ=1時(shí),λ可省略不寫.在[Ars Combin.,2010,96:321-329]中已經(jīng)得到了LS_λ(K_(1,2),K_(v,v))的存在譜.本文證明了當(dāng)v≡4(mod 12)時(shí),存在LS(F,K_(v,v,v)),這里F∈{K_(1,3),K_(2,2)}.
[Abstract]:Let G be a finite graph and H be a subgraph of G. If V (H) = V (G), then H is the generated subgraph of G. A 位 fold F- factor of a graph G, denoted as S _ 位 (FG), is a generated subgraph of G and can be broken down into the union of several subgraphs isomorphic to F (called F-domain group). So that each vertex in the V (G) appears in the 位 -block. The 位 -factor set of a graph G, denoted as LS_ 位 (FG), is a partition {Bi} of all subgraphs of G which are isomorphic to F, such that each BCI constitutes a S _ 位 (FG). When 位 = 1, 位 can be omitted and not written. In [Ars Combin.,2010,96:321-329], we have obtained the existence spectrum of LS_ 位 (K _ (1N _ 2), K _ (v). In this paper, it is proved that there exists LS (F ~ (K _ (v), where F 鈭，

本文編號(hào)：2428591