منابع مشابه
Decomposing Weighted Graphs
We solve the following problem: Can an undirected weighted graph G be partitioned into two non-empty induced subgraphs satisfying minimum constraints for the sum of edge weights at vertices of each subgraph? We show that this is possible for all constraints a(x), b(x) satisfying dG(x) ≥ a(x) + b(x) + 2WG(x), for every vertex x, where dG(x),WG(x) are, respectively, the sum and maximum of inciden...
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It was conjectured by Hoffmann-Ostenhof that the edge set of every cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. We prove the conjecture for 3-connected cubic plane graphs and 3-connected cubic graphs on the projective plane. Our proof provides a polynomial time algorithm to find the decomposition for 3-connected cubic plane graphs.
متن کاملDecomposing infinite graphs
In his classic paper Über eine Eigenschaft der ebenen Komplexe, Wagner [ 19 ] tackles the following problem. Kuratowski’s theorem, in its excluded minor version, states that a finite graph is planar if and only if it has no minor isomorphic to K5 or to K3,3. (A minor of G is any graph obtained from some H ⊂ G by contracting connected subgraphs.) If we exclude only one of these two minors, the g...
متن کاملDecomposing Graphs with Symmetries
While decomposing graphs in simpler items greatly helps to design more efficient algorithms, some classes of graphs can not be handled using the classical techniques. We show here that a graph having enough symmetries can be factored into simpler blocks through a standard morphism and that the inverse process may be formalized as a pullback rewriting system.
متن کاملDecomposing Graphs into Long Paths
It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C3, C4, C5, and K4 − e have no such decompositions. We construct an infinite sequence {Fi}∞i=0 of nondecomposable graphs. On the other hand, we prove that every...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2017
ISSN: 0364-9024
DOI: 10.1002/jgt.22124