Graph theory analysis of complex brain networks: New concepts in brain mapping applied to neurosurgery Neuroanatomy has entered a new era, culminating in the search for the connectome, otherwise known as the brain's wiring diagram. While this approach has le... M.G. Hart,R.J.F. Ypma,R Ro...
Given a graph G, let fG(n,m) be the minimal number k such that every k independent n-sets in G have a rainbow m-set. Let D(2) be the family of all graphs with maximum degree at most two. For t≥3, let Ct be the cycle with vertex set [1,t] and edge set {12,23,…,(...
Harary, F., "Independent discoveries in graph theory", Annals of the New York Academy of Sciences, Vol. 328, No. 1, 1979, 1-4.F. Harary, "Independent discoveries in graph theory", Annals of the New York Academy of Sciences, Volume 328 Number 1 (1979), pages 1-4....
Rainbow independent sets in graphs with maximum degree two Given a graph $G$, let $f_{G}(n,m)$ be the minimal number $k$ such that every $k$ independent $n$-sets in $G$ have a rainbow $m$-set. Let $\\mathcal{D}(2)$... Y Ma,X Hou,J Gao,... 被引量: 0发表: 2021...
Füredi, Z.: The number of maximal independent sets in connected graphs. J. Graph Theory 11(4), 463–470 (1987) Article MATH MathSciNet Google Scholar Griggs, J.R., Grinstead, C.M., Guichard, D.R.: The number of maximal independent sets in a connected graph. Discrete Math. 68(...
对图G顺利染色所需要的最小的k称色数(chronic number),记为χ(G)。 Remark 只要k取得足够大,整张图肯定是可以被顺利染色的,比如一个结点取一个颜色,k=n。所以我们更关心图上最小需要几种颜色才可以被顺利染色,也就是\chi(G)的值。 \chi(G)=2当且仅当图是一个二分图。 四色定理说,平面图的\chi(G...
We use an entropy based method to study two graph maximization problems. We upper bound the number of matchings of fixed size in a d-regular graph on N ve... T Carroll,D Galvin,P Tetali - 《Journal of Combinatorial Theory》 被引量: 62发表: 2012年 Independent Sets, Matchings, and Occu...
In this paper,we prove that if α(G) ≤(4b(δ(G)-b+1))/((a+1)2+4b),then G is fractional ID-[a, b]-factor-critical.关键词: independent number minimum degree fractional [a b]-factor fractional ID-[a b]-factor-critical
Füredi, Z.: The number of maximal independent sets in connected graphs. J. Graph Theory 11, 463–470 (1987) Article MathSciNet MATH Google Scholar Jin, Z., Li, X.: Graphs with the second largest number of maximal independent sets. Discrete Math. 308, 5864–5870 (2008) Article Math...
Many important theorems in combinatorics, such as Szemer\'edi's theorem on arithmetic progressions and the Erd\H{o}s-Stone Theorem in extremal graph theory, can be phrased as statements about independent sets in uniform hypergraphs. In recent years, an important trend in the area has been to...