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For a graph G with vertices labeled 1, 2, …, n and a permutation α in Sn, the symmetric group on {1, 2, …, n}, the α-generalized prism over G, α(G), consists of two copies of G, say Gx and Gy, along with the edges (xi, yα(i)), for 1 ≤ i ≤ n. In this note, we consider results of the form that if G has property P, then for any α ∈ S∣V (G)∣, α(G) is supereulerian. We proved that if a graph G is 2-edge-connected...
For two integers s ges 0 and t ges 0, G is (s,t)-supereulerian, if for every two disjoint edge-sets X sub E(G) and Y sub E(G), with |X| les s and |Y| les t, G has a spanning eulerian subgraph H with X sub E(H) and Y cap E(H) = 0. Clearly, G is supereulerian if and only if G is (0,0)-supereulerian. Here it is proved that if G is a (2 + t)-edge-connected triangle-free simple graph on n vertices with...
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