MOD (2p+1)-ORIENTATION ON BIPARTITE GRAPHS AND COMPLEMENTARY GRAPHS
MOD (2p+1)-ORIENTATION ON BIPARTITE GRAPHS AND COMPLEMENTARY GRAPHS
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MOD (2p 1)-二分图和补图的方向
DOI：
10.1137/16m106889x
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发表时间：
2018
影响因子：
0.8
通讯作者：
Hong-Jian Lai
中科院分区：
文献类型：
--
作者：
Jiaao Li;Xinmin Hou;Miaomiao Han;Hong-Jian Lai
A mod (2p + 1)-orientation D is an orientation of G such that d(D)(+)(v) - d(D)(-)(v) equivalent to 0 (mod 2p + 1) for any vertex v is an element of V(G). Jaeger conjectured that every 4p-edge-connected graph has a mod (2p + 1)-orientation. A graph G is strongly Z(2p+1)-connected if for every mapping b : V(G) (bar right arrow) Z(2p +1) with Sigma(v is an element of V(G)) b(v) = 0, there exists an orientation D of G such that d(D)(+)(v) - d(D)(-)(v) = b(v) in Z(2p+1) for any v is an element of V(G). A strongly Z(2p+1)-connected graph admits a mod (2p + 1)-orientation, and it is a contractible configuration for mod (2p +1)-orientation. We prove Jaeger's module orientation conjecture is equivalent to its restriction to bipartite simple graphs and investigate strongly Z(2p+1)-connectedness of certain bipartite graphs, particularly for p = 2. We also show that if G is a simple graph with vertical bar V(G)vertical bar >= N(p) = 1152p(4) and min{delta(G),delta(G(c))} >= 4p, then either G or G(c) is strongly Z(2p+1)-connected. When p = 2, the value of N(2) can be reduced to N(2) = 80.
