Even-hole-free graphs part I: Decomposition theorem. Journal of Graph Theory, 39(1):6-49, 2002.M. Conforti, G. Cornuejols, A. Kapoor, and K. Vušković. Even-hole- free graphs Part I : Decomposition 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...
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 [...
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...
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...
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 ...
Rook polynomials are a powerful tool in the theory of restricted permutations. It is known that the rook polynomial of any board can be computed recursively, using a cell decomposition technique of Riordan. In this paper, we give a new decomposition theorem, which yields a more efficient ...
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 ...
(cf. Theorem2.5). This result applies even ifis noncompact. For the particular case of global nonnegativity,, we immediately recover a sparse-matrix version of Reznick’z Positivestellensätz [39] (cf. Theorem2.3), and further prove a version of the Hilbert–Artin theorem [5] where the ...
Second, the subband decomposition of the signal spectrum leads naturally to multiresolution signal decomposition via multirate signal processing in accordance with the Nyquist sampling theorem. Apart from coding/compression considerations, signal decomposition into subbands permits us to investigate the ...