Author's Personal Copy Discrete Applied Mathematics on Strongly Z 2s+1 -connected Graphs
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چکیده
An orientation of a graph G is a mod(2s + 1)-orientation if under this orientation, the net out-degree at every vertex is congruent to zero mod(2s + 1). If for any function b : V (G) → Z2s+1 satisfying v∈V (G) b(v) ≡ 0 (mod 2s + 1), G always has an orientation D such that the net out-degree at every vertex v is congruent to b(v) mod (2s + 1), then G is strongly Z2s+1-connected. In this paper, we prove that a connected graph has a mod(2s+1)-orientation if and only if it is a contraction of a (2s+1)-regular bipartite graph. We also proved that every (4s−1)-edge-connected series–parallel graph is stronglyZ2s+1connected, and every simple 4p-connected chordal graph is strongly Z2s+1-connected. © 2014 Elsevier B.V. All rights reserved.
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