It is known[5] that an investigation of the up-embeddability of the 3-regular graphs shows a useful approach to that of the general graph. But as far, very few characterizations of the upembeddability are known on the...It is known[5] that an investigation of the up-embeddability of the 3-regular graphs shows a useful approach to that of the general graph. But as far, very few characterizations of the upembeddability are known on the 3-regular graphs. Let G be a 2-edge connected 3-regular graph.We prove that G is up-embeddable if and only if G can be obtained from the graphs θ, θ or K4by a series of M- or N-extensions. Meanwhile, we also present a new structural characterization of such graph G provided that G is up-embeddable.展开更多
文摘It is known[5] that an investigation of the up-embeddability of the 3-regular graphs shows a useful approach to that of the general graph. But as far, very few characterizations of the upembeddability are known on the 3-regular graphs. Let G be a 2-edge connected 3-regular graph.We prove that G is up-embeddable if and only if G can be obtained from the graphs θ, θ or K4by a series of M- or N-extensions. Meanwhile, we also present a new structural characterization of such graph G provided that G is up-embeddable.
