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Let be the circular flow number of a bridgeless graph . By Steffen it was proved that, for a bridgeless ‐regular graph , where is a positive integer, if and only if has a perfect matching such that is bipartite. This implies that is a class 1 graph. For , all graphs with circular flow number bigger than...
The resistance r(G) of a graph G is the minimum number of edges that have to be removed from G to obtain a graph which is Δ(G)-edge-colorable. This paper relates the resistance to other parameters that measure how far a graph is from being Δ-edge-colorable. Let rv(G) be the minimum number of vertices that have to be removed from G to obtain a class 1 graph. We show that r(G)rv(G)≤⌊Δ(G)2⌋, and that...
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