NOTE - On circular flows of graphs
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چکیده
Here, we give a simple proof of this theorem without using linear programming. Proof. Since G is 6-edge-connected, by Tutte [5, Theorem 1] or NashWilliams [4, Theorem 1], let T1,T2,T3 be three edge disjoint spanning trees of G. Let Pi be a parity subgraph of Ti (for i=1,2 only). Now fixing some orientation of G. Since P1∪P2 and G\E(P1) are even graphs, let f1 be a nowhere-zero 2-flow with support E(P1)∪E(P2) and f2 be a nowhere-zero 2-flow with support E(G)\E(P1). Then f=f1+2f2 is a nowhere-zero 4-flow of G. Reorient the edges of G such that the resulting correspondent 4-flow f∗>0. We will show this is the required orientation. First, this orientation is
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تاریخ انتشار 2003