P_n~k的均匀全染色

设G(V,E)是一个简单图,f是G的一个k-正常全染色,若f满足||Vi∪Ei|-|Vj∪Ej||≤1(i≠j),其中Vi∪Ei={v|f(v)=i}∪{e|f(e)=i},则称f为G的k-均匀全染色,简记为k-ETC.并称eχT(G)=min{k|G存在k-均匀全染色}为G的均匀全染色数.本文将通过很好的全染色方法得到eχT(Pkn)=5(n≥2k+1),并证明了对Pkn,[5]中猜想是正确的.     

Facets of the balanced (acyclic) induced subgraph polytope

A signed graph is a graph whose edges are labelled positive or negative. A signed graph is said to be balanced if the set of negative edges form a cut. The balanced induced subgraph polytopeP(G) of a graphG is the convex hull of the incidence vectors of all node sets that induce balanced subgraphs ofG. In this paper we exhibit various (rank) facet defining inequalities. We describe several methods with which new facet defining inequalities ofP(G) can be constructed from known ones. Finding a maximum weighted balanced induced subgraph of a series parallel graph is a polynomial problem. We show that for this class of graphsP(G) may have complicated facet defining inequalities. We derive analogous results for the polytope of acyclic induced subgraphs.Research supported in part by the Natural Sciences and Engineering Research Council of Canada; the second author has also been supported by C.P. Rail.     

A Range-Compaction Heuristic for Graph Coloring

This paper presents a novel heuristic for graph coloring that works on a range of colors and iteratively tries to make this range more compact. This range-compaction heuristic also has a pressure component and an annealing schedule for it. The value of this component is empirically quantified. This algorithm is evaluated on a wide range of DIMACS benchmark graphs, and found to be competitive with state-of-the-art algorithms in terms of solution quality and run time.     

推广的Mycielski图和类推广的Mycielski图的(邻点可区别的)全染色

Mycielski图是在1955年由Mycielski首先提出的,推广的Mycielski图是在2003年由Peter Che Bor Lam,林文松等给出的Mycielski图的一个自然推广,且研究了它的圆色数.目前关于推广的Mycielski图性质以及它们在点色数,分数色数,圆色数等方面已有许多研究.本文定义了推广的Mycielski图的另一推广称为类推广的Mycielski图,且探讨了推广的Mycielski图和类推广的Mycielski图在全染色、邻点可区别全染色方面与原基础图的关系,从而也得到了它们满足全染色猜想和邻点可区别全染色猜想及它们达到全色数和邻点可区别的全色数的下界的一些充分条件.     

极大外平面图的关联色数

简要介绍了图的关联着色问题的起源、发展情况及目前已有的结论，对一类特殊的图——极大外平面图(△≠6)，给出了其关联色数．     

Mycielski图的BBC染色

基于图G的Mycielski图M（G）,研究xb（G,TG）与xb（M（G）,T’）之间的关系以及xb（G,TG）与xb（M（G）,T＂）之间的关系,其中Tc为G的生成树,T’,T＂分别为M（G）的两类特殊生成树．并给出当G为二部图,完全图以及Halin图时,Xb（M（G）,T＂）的值．     

一些图的倍图与Mycielski图的邻点可区别VE-全染色

对简单图G(V,E),存在一个正整数κ,使得映射f:V(G)U E(G)→{1,2…,κ},如果对uv∈E(G),有f(u)≠f(uv),f(v)≠f(uv),且C(u)≠C(v),则称f是图G的邻点可区别VE-全染色,且称最小的数κ为图G的邻点可区别VE-全色数,讨论了路、圈、星、扇、轮等一些图的倍图与Mycielski图的邻点可区别VE-全色数。     

完全二部图的广义Mycielski图的全染色与边染色

为了找到Km,n图的广义Mycielski图的全色数与边色数,用分析的方法,考虑不同情况,给出了它的全染色法与边染色法,得到了它的全色数与边色数.     

广义Peterson图的邻点可区别的全染色

设P_(n,k)是一个简单图,其顶点集和边集分别为:V(P_(n,k))={u_0,u_1,…u_(n-1),v_0,v_1,…v_(n-1)},E(P_(n,k))={u_iu_(i+1),u_iv_i,v_iv_(1+k)},则称P_(n,k)为广义Peterson图,其中n≥5,0相似文献   

关于图的均匀全色数分类

对一个正常的全染色满足各种颜色所染元素数(点或边)相差不超过1时,称为均匀全染色,其所用最少染色数称为均匀全色数.将图按均匀全色数分类,证明了简单图在若干情况下的均匀全色数定理,得到了一些联图的均匀全色数.     

New Results on the Queens_n 2 Graph Coloring Problem

For the Queens_n ² graph coloring problems no chromatic numbers are available for n > 9 except where n is not a multiple of 2 or 3. In this paper we propose an exact algorithm that takes advantage of the particular structure of these graphs. The algorithm works on the independent sets of the graph rather than on the vertices to be colored. It combines branch and bound, for independent set assignment, with a clique based filtering procedure. A first experimentation of this approach provided the coloring number values ranging for n = 10 to n = 14.     

Polyhedral studies on the convex recoloring problem

A coloring of the vertices of a graph G is convex if, for each assigned color d, the vertices with color d induce a connected subgraph of G. We address the convex recoloring problem, defined as follows. Given a graph G and a coloring of its vertices, recolor a minimum number of vertices of G, so that the resulting coloring is convex. This problem is known to be NP-hard even when G is a path. We show an integer programming formulation for the weighted version of this problem on arbitrary graphs, and then specialize it for trees. We study the facial structure of the polytope defined as the convex hull of the integer points satisfying the restrictions of the proposed ILP formulation, present several classes of facet-defining inequalities and discuss separation algorithms.     

若干倍图的均匀全染色(英文)

如果图G的一个正常全染色满足任意两种颜色所染元素(点或边)数目相差不超过1,则称为G的均匀全染色,其所用最少染色数称为均匀全色数.本文得到了星、扇和轮的倍图的均匀全色数.     

外平面图的全染色与列表全染色

本文证明了,如果G是满足条件Δ(G)≥4的外平面图,则x_T~L(G)=Δ(G) 1,同时对Δ(G)=3给出了XT(G)=Δ(G) 1的简短的新证明,从而蕴含Δ(G)≥3时,XT(G)=Δ(G) 1,其中XT(G)是G的点边全色数,x_T~L(G)是G的点边列表全色数。     

图M（Pn）和M（Gn）的点可区别均匀边染色

用构造法研究了路和圈的Mycielski图的点可区别均匀边染色,得到了路和圈的Mycielski图的点可区别均匀边色数,验证了它们满足点可区别均匀边染色猜想（VDEECC）．     

扇的倍图的邻点可区别边色数

设G(V,E)是阶数至少是3的简单连通图,若f是图G的k-正常边染色,使得对任意的uv∈E(G),C(u)≠C(v),那么称f是图G的k-邻点可区别边染色(k-ASEC),其中C(u)={f(uw)│uw∈E(G)},而χa′s(G)=min{k│存在G的一个k-ASEC},称为G的邻点可区别边色数.本文给出扇的倍图D(Fm)的邻点可区别边色数.     

星和完全等二部图联图的点可区别均匀边染色

研究了星与完全等二部图的联图Sm∨Kn,n的点可区别均匀边染色。     

若干Mycielski's图的邻点可区别E-全染色

针对简单图G与Mycielski's图之间的关系,讨论了路、圈、星、扇、轮和完全图的Mycielski's图的邻点可区别E-全染色,给出了路、圈、星、扇、轮和完全图的Mycielski's图的邻点可区别E-全色数.     

Graph Coloring with Adaptive Evolutionary Algorithms

This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EAs). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no domain specific knowledge, except, of course, from the decoder (fitness function). We compare this adaptive EA to a powerful traditional graph coloring technique DSatur and the Grouping Genetic Algorithm (GGA) on a wide range of problem instances with different size, topology and edge density. The results show that the adaptive EA is superior to the Grouping (GA) and outperforms DSatur on the hardest problem instances. Furthermore, it scales up better with the problem size than the other two algorithms and indicates a linear computational complexity.     

Facets of the independent set polytope

Theoretical results pertaining to the independent set polytope P^ISP=conv{x{0,1}ⁿ:Axb} are presented. A conflict hypergraph is constructed based on the set of dependent sets which facilitates the examination of the facial structure of P^ISP. Necessary and sufficient conditions are provided for every nontrivial 0-1 facet-defining inequalities of P^ISP in terms of hypercliques. The relationship of hypercliques and some classes of knapsack facet-defining inequalities are briefly discussed. The notion of lifting is extended to the conflict hypergraph setting to obtain strong valid inequalities, and back-lifting is introduced to strengthen cut coefficients. Preliminary computational results are presented to illustrate the usefulness of the theoretical findings.Mathematics Subject Classification (2000): 90C11, 90C57, 90C35