graph decomposition): 图G 有分式F 分解,存在图 G 的一个非负F 重量函数 ω:KF→[0,∞) ,其中 KF 为G 的所有同构 F 的子图,使得对任意的 e∈E(G) 有: ∑F′:e∈E(F)ω(F′)=1. Remark: 如果我们要求图分解的 F 重量函数为ω:KF→{0,1}. 则分式 F 分解为 F分解。 Theorem [...
对任意的p>0, 存在c>0,h\in \mathbb{N},对于任何充分大的偶数d正则的(c,h,p)typical 图G,都可以分解成任何给定的d/2个2因子。 现在考虑超图版本的"大图"分解。 当F为超图的1因子(超图中的完美匹配)时: Theorem [Baranyai 1975][8] Knk有1因子分解 当且仅当k∣n。 考虑...
Even-hole- free graphs part I: Decomposition theorem. Journal of Graph Theory, 39(1):6-49, 2002.Conforti, M., Cornuéjols, G., Kapoor, A., Vušković, K.: Even-hole-free graphs, Part I: decomposition theorem. J. Graph Theory 39 , 6–49 (2002) View Article MATH MathSciNet...
We develop a polynomial-time algorithm using topological graph theory to decompose a graph into the structure guaranteed by the theorem: a clique-sum of pieces almost-embeddable into bounded-genus surfaces. This result has many applications. In particular we show applications to developing many ...
Sign in to download full-size image Figure 5.8. An illustration of the decomposition algorithm. Theorem 5.24 (Golumbic [1977a]) Let A be an implication class of an undirected graph G = (V, E), and let D be an implication class of E−A^. Either (i) D is an implication class of...
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat Mach Intel. 2021;3(3):218–29. Article Google Scholar Luo L, Shiu WS, Chen R, Cai XC. A nonlinear elimination preconditioned inexact Newton method for blood flow problems in human artery ...
theorem, decomposition of multiparameter modules is known to be unstable in a certain precise sense. until now, it has not been clear that there is any way to get around this and build a meaningful stability theory for multiparameter module decomposition. we introduce new tools, in particular ...
Singular Value Decomposition (SVD) is widely used in linear algebra and is known for its strength, particularly arising from the fact that every matrix has an SVD. It looks like this: For our purposes, let's suppose , , , and , and that U, V are orthogonal matrices, whereas ∑ is a...
Theorem 1 Let G=(V,E) be a graph and TG=({Xi|i∈I},T) a tree decomposition of G. Let u,v∈V, and ru (resp. rv) be the root node of the induced subtree of u (resp. v). Then for every node w in SPru,rv, there is one vertex t∈Xw, such that sdist(u,v)=sdist(u...
Theorem 1.4 (Theorem 5.7) Both weak combinatorial invariance conjectures as suggested in Conjecture 5.2 and Conjecture 5.3 are valid in the case of permutation groups. 1.2 Methods of proof Our main line of study revisits the theory of Dyer-Lehrer [6] for Hecke algebras. Recall that Kazhdan–Lu...