导出匹配问题的NP-完全性以及导出匹配可扩问题的CO-NP-完全性

图Ｇ的一个匹配Ｍ是导出的,若Ｍ是图Ｇ的一个导出子图。图Ｇ是导邮匹配可扩的（简记ＩＭ－可扩的）,若图Ｇ的任一导出匹配均含于图Ｇ的一个完美匹配当中。本文我们将证明如下结果。⑴对无爪图而言,问题“给定图Ｇ以及一个正整数ｒ,确定是否存在图Ｇ的一个导出匹配Ｍ使得Ｍ≥ｒ”是ＮＰ－完全的。⑵对直径为２的图以及直径为３的偶图,问题“确定一个给定图是否为导出匹配可扩的”是ＣＯ－ＮＰ完全的;而对完全多部图而言,问题“     

3-正则图的分割问题是NP-完全问题

证明了3-正则图的最小平分问题和最小α-分割问题都是NP-完全问题.     

符号混合控制问题的某些NP-完全性结果

Let G =(V, E) be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f:V∪E→ {-1, 1} such that ∑_(y∈N_m(x)∪{x})f(y)≥ 1for every element x∈V∪E, where N_m(x) is the set of elements of V∪E adjacent or incident to x. The weight of f is w(f) =∑_(x∈V∪E)f(x). The signed mixed domination problem is to find a minimum-weight signed mixed dominating function of a graph. In this paper we study the computational complexity of signed mixed domination problem. We prove that the signed mixed domination problem is NP-complete for bipartite graphs, chordal graphs, even for planar bipartite graphs.     

偶图的补图的侧廓问题和填充问题的NP-完全性

本文研究偶补图的侧廓问题和填充问题的计算复杂性，证明了：即使对直径不超过2的偶补图，侧廓问题和填充问题也是NP－完全的．     

一个具有两类工件的多目标排序的NP-困难性

文章考虑具有两个工件集的单机排序问题.第一个工件集J1以加权完工时间和为目标函数,第二个工件集J2以最大加权完工时间为目标函数.问题的目标是寻找一种排序,使得两个目标函数的加权和达到最小,并证明该问题是强NP-困难的.     

图的部分控制集问题的修正 Greedy算法

部分控制集问题是对于给定的顶点赋权图G=(V,E;c)和正整数K,寻找图G一个顶点子集T,使得在其控制下的顶点个数不小于K且T中顶点权和达到最小。本文讨论了部分控制集问题的NP-困难性;给出了该问题的一种修正Greedy近似算法,并对其近似度H(K)给出了证明。     

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.     

完全二部图的符号星控制数

近年来,研究图的符号星控制数颇引人注目,研究了完全二部图的符号星控制数.     

直径为5的图的2-导出匹配划分和2-导出匹配覆盖问题的NP-完全性

给定一个简单图G和正整数κ,具有完美匹配的图G的κ-导出匹配划分是对顶点集V(C)的一个κ-划分(V1,V2,...,Vκ),其中对每一个i(1≤i≤κ),由Vi导出的G的子图G[Vi]是1-正则的.κ-导出匹配划分问题是指对给定的图G,判定G是否存在一个κ-导出匹配划分.令M1,M2…,Mκ为图G的κ个导出匹配,如果V(M1)UV(M2)∪...∪V(Mκ)=V(G),则我们称{M1,M2,...,Mκ}是G的κ-导出匹配覆盖.κ-导出匹配覆盖问题是指对给定的图G,判定G是否存在κ-导出匹配覆盖.本文给出了Yang,Yuan和Dong所提出问题的解,证明了直径为5的图的导出匹配2一划分问题和导出匹配2-覆盖问题都是NP-完全的.     

两类只含整数根的色多项式

研究了两类只含整数根的色多项式,给出其相应图G为弦图的必要条件,并完全刻画了G的色等价类[G].     

Total domination in planar graphs of diameter two

MacGillivary and Seyffarth [G. MacGillivray, K. Seyffarth, Domination numbers of planar graphs, J. Graph Theory 22 (1996) 213–229] proved that planar graphs of diameter two have domination number at most three. Goddard and Henning [W. Goddard, M.A. Henning, Domination in planar graphs with small diameter, J. Graph Theory 40 (2002) 1–25] showed that there is a unique planar graph of diameter two with domination number three. It follows that the total domination number of a planar graph of diameter two is at most three. In this paper, we consider the problem of characterizing planar graphs with diameter two and total domination number three. We say that a graph satisfies the domination-cycle property if there is some minimum dominating set of the graph not contained in any induced 5-cycle. We characterize the planar graphs with diameter two and total domination number three that satisfy the domination-cycle property and show that there are exactly thirty-four such planar graphs.     

Improved bottleneck domination algorithms

W.C.K. Yen introduced BOTTLENECK DOMINATION and BOTTLENECK INDEPENDENT DOMINATION. He presented an -time algorithm to compute a minimum bottleneck dominating set. He also obtained that the BOTTLENECK INDEPENDENT DOMINATING SET problem is NP-complete, even when restricted to planar graphs.We present simple linear time algorithms for the BOTTLENECK DOMINATING SET and the BOTTLENECK TOTAL DOMINATING SET problem. Furthermore, we give polynomial time algorithms (most of them with linear time-complexities) for the BOTTLENECK INDEPENDENT DOMINATING SET problem on the following graph classes: AT-free graphs, chordal graphs, split graphs, permutation graphs, graphs of bounded treewidth, and graphs of clique-width at most k with a given k-expression.     

NP-completeness results for edge modification problems

The aim of edge modification problems is to change the edge set of a given graph as little as possible in order to satisfy a certain property. Edge modification problems in graphs have a lot of applications in different areas, and many polynomial-time algorithms and NP-completeness proofs for this kind of problems are known. In this work we prove new NP-completeness results for these problems in some graph classes, such as interval, circular-arc, permutation, circle, bridged, weakly chordal and clique-Helly graphs.     

Independent domination in triangle-free graphs

Let G be a simple graph of order n and minimum degree δ. The independent domination numberi(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. We establish upper bounds, as functions of n and δ?n/2, for the independent domination number of triangle-free graphs, and over part of the range achieve best possible results.     

Efficient edge domination in regular graphs

An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p≥3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete.     

Strong clique trees,neighborhood trees,and strongly chordal graphs

Maximal complete subgraphs and clique trees are basic to both the theory and applications of chordal graphs. A simple notion of strong clique tree extends this structure to strongly chordal graphs. Replacing maximal complete subgraphs with open or closed vertex neighborhoods discloses new relationships between chordal and strongly chordal graphs and the previously studied families of chordal bipartite graphs, clique graphs of chordal graphs (dually chordal graphs), and incidence graphs of biacyclic hypergraphs. © 2000 John Wiley & Sons, Inc. J. Graph Theory 33: 151–160, 2000     

Signed and minus domination in bipartite graphs

The paper studies the signed domination number and the minus domination number of the complete bipartite graph K _{p, q} .