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- W2475350901 abstract "Throughout this paper, all graphs are assumed to be embedded into an orientable surface. A graph is Eulerian if the degree of every vertex is even. An Eulerian graph is separating if the regions into which the surface is divided by the graph are 2-colorable. Let G be a graph and G its dual. We show an identity which relates the generating function of Eulerian subgraphs of G and the generating function of separating Eulerian subgraphs of G. 1. Eulerian subgraphs We define a graph G as a triple (V (G),E(G), G), where V (G) and E(G) are finite sets and G : E(G) ! V (G) ◊ V (G). The elements of V (G) and E(G) are called the vertices and edges, respectively, of G. i(e) and t(e) are defined by G(e) = (i(e),t(e)) for e 2 E(G); we say that the vertices i(e) and t(e) are on the edge e, and the edge e are on the vertices i(e) and t(e). The degree, deg G ( ), in G of a vertex 2 V (G) is #{e 2 E(G) | i(e) = } + #{e 2 E(G) | t(e) = }. A graph is Eulerian if the degree of every vertex is even. A subgraph H of G is a graph containing a subset of the edges of G and those vertices of G which on these edges. A subgraph H of G is Eulerian if the graph H is Eulerian. E(G) denotes the collection of all Eulerian subgraphs of G. Let u = {u(e) | e 2 E(G)} be a set of commutative indeterminates. A polynomial" @default.
- W2475350901 created "2016-07-22" @default.
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- W2475350901 date "2002-01-01" @default.
- W2475350901 modified "2023-09-27" @default.
- W2475350901 title "GENERATING FUNCTIONS OF EULERIAN AND SEPARATING" @default.
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