共查询到20条相似文献,搜索用时 31 毫秒
1.
Jing-wen Li Zhi-wen Wang Jaeun Lee Moo Young Sohn Zhong-fu Zhang En-qiang Zhu 《应用数学学报(英文版)》2010,26(3):525-528
In this paper we get some relations between α(G), α'(G), β(G), β'(G) and αT(G), βT(G). And all bounds in these relations are best possible, where α(G), α'(G),/3(G), β(G), αT(G) and βT(G) are the covering number, edge-covering number, independent number, edge-independent number (or matching number), total covering number and total independent number, respectively. 相似文献
2.
Pekka Salmi 《Semigroup Forum》2010,80(1):155-163
Let G be a locally compact group and LUC(G) the C*-algebra of the bounded left uniformly continuous functions on G. The spectrum G
LUC of LUC(G) is the universal semigroup compactification of G with respect to the joint continuity property: the multiplication on G×G
LUC is jointly continuous. The paper studies the joint weak* continuity of multiplication on LUC(G)* and, in particular, the question how the joint continuity property of G
LUC can be related to a property concerning the whole algebra LUC(G)*. The group G is naturally replaced by the measure algebra M(G), and LUC(G)* can be identified with M(G
LUC), the space of regular Borel measures on G
LUC. It is shown that the joint weak* continuity can fail even on bounded sets of M(G)×M(G
LUC), but, on the other hand, the multiplication on M(G)×M(G
LUC) is positive continuous in the sense of Jewett. 相似文献
3.
The amenability of the Banach algebra L
1(G), the measure algebra M(G) and their second duals of a locally compact group have been considered by a number of authors. During these investigations it has been shown that L
1(G)** is amenable if and only if G is finite. If LUC (G)*, the dual of the space of left uniformly continuous functions on G, is amenable, then G is compact and M(G) is amenable. Finally, if M(G)** is amenable, then G is finite. The aim of this paper is to generalize all of the above results to the locally compact hypergroups. 相似文献
4.
For a graph G, the cochromatic number of G, denoted z(G), is the least m for which there is a partition of the vertex set of G having order m. where each part induces a complete or empty graph. We show that if {Gn} is a family of graphs where Gn has o(n2 log2(n)) edges, then z(Gn) = o(n). We turn our attention to dichromatic numbers. Given a digraph D, the dichromatic number of D is the minimum number of parts the vertex set of D must be partitioned into so that each part induces an acyclic digraph. Given an (undirected) graph G, the dichromatic number of G, denoted d(G), is the maximum dichromatic number of all orientations of G. Let m be an integer; by d(m) we mean the minimum size of all graphs G where d(G) = m. We show that d(m) = θ(m2 ln2(m)). 相似文献
5.
Let S be a finite linear space, and letG be a group of automorphisms of S. IfG is soluble and line-transitive, then for a givenk but a finite number of pairs of (S, G),S hasv= p
n
points andG ⩽AΓL(1,p
n
). 相似文献
6.
Martin Kochol 《Journal of Graph Theory》2002,40(3):137-146
The tension polynomial FG(k) of a graph G, evaluating the number of nowhere‐zero ?k‐tensions in G, is the nontrivial divisor of the chromatic polynomial χG(k) of G, in that χG(k) = kc(G)FG(k), where c(G) denotes the number of components of G. We introduce the integral tension polynomial IG(k), which evaluates the number of nowhere‐zero integral tensions in G with absolute values smaller than k. We show that 2r(G)FG(k)≥IG(k)≥ (r(G)+1)FG(k), where r(G)=|V(G)|?c(G), and, for every k>1, FG(k+1)≥ FG(k)˙k / (k?1) and IG(k+1)≥IG(k)˙k/(k?1). © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 137–146, 2002 相似文献
7.
Tsuyoshi Nishimura 《Journal of Graph Theory》1989,13(1):63-69
We show that if r ? 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ? (r + 1)2/2 and (r + 1)2α(G) ? 4rk(G), then G has an r-factor; if r ? 2 is even and G is a graph with k(G) ? r(r + 2)/2 and (r + 2)α(G) ? 4k(G), then G has an r-factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively). 相似文献
8.
For a pair of integers k, l≥0, a graph G is (k, l)‐colorable if its vertices can be partitioned into at most k independent sets and at most l cliques. The bichromatic number χb(G) of G is the least integer r such that for all k, l with k+l=r, G is (k, l)‐colorable. The concept of bichromatic numbers simultaneously generalizes the chromatic number χ(G) and the clique covering number θ(G), and is important in studying the speed of hereditary properties and edit distances of graphs. It is easy to see that for every graph G the bichromatic number χb(G) is bounded above by χ(G)+θ(G)?1. In this article, we characterize all graphs G for which the upper bound is attained, i.e., χb(G)=χ(G)+θ(G)?1. It turns out that all these graphs are cographs and in fact they are the critical graphs with respect to the (k, l)‐colorability of cographs. More specifically, we show that a cograph H is not (k, l)‐colorable if and only if H contains an induced subgraph G with χ(G)=k+1, θ(G)=l+1 and χb(G)=k+l+1. © 2010 Wiley Periodicals, Inc. J Graph Theory 65: 263–269, 2010 相似文献
9.
P. Papasoglu 《Geometriae Dedicata》1995,54(3):301-306
We prove that any two locally finite homogeneous trees with valency greater than 3 are bilipschitz equivalent. This implies that the quotienth
1(G)/h
k
(G), whereh
k
(G) is thekthL
2-Betti number ofG, is not a quasi-isometry invariant. 相似文献
10.
The computation of the projective surgery obstruction groupsL
n
p
(ZG), forG a hyperelementary finite group, is reduced to standard calculations in number theory, mostly involving class groups. Both the exponent of the torsion subgroup and the precise divisibility of the signatures are determined. ForG a 2-hyperelementary group, theL
n
p
(ZG) are detected by restriction to certain subquotients ofG, and a complete set of invariants is given for oriented surgery obstructions.Partially supported by NSERC grant A4000.Partially supported by NSF grant DMS-8610730(1) and the Danish Research Council. 相似文献
11.
Richard C. Bradley 《Journal of Graph Theory》2006,51(3):251-259
For a given snark G and a given edge e of G, let ψ(G, e) denote the nonnegative integer such that for a cubic graph conformal to G – {e}, the number of Tait colorings with three given colors is 18 · ψ(G, e). If two snarks G1 and G2 are combined in certain well‐known simple ways to form a snark G, there are some connections between ψ (G1, e1), ψ (G2, e2), and ψ(G, e) for appropriate edges e1, e2, and e of G1, G2, and G. As a consequence, if j and k are each a nonnegative integer, then there exists a snark G with an edge e such that ψ(G, e) = 2j · 3k. © 2005 Wiley Periodicals, Inc. 相似文献
12.
The geodetic numbers of graphs and digraphs 总被引:1,自引:0,他引:1
Chang-hong LU~ 《中国科学A辑(英文版)》2007,50(8):1163-1172
For every two vertices u and v in a graph G,a u-v geodesic is a shortest path between u and v.Let I(u,v)denote the set of all vertices lying on a u-v geodesic.For a vertex subset S,let I(S) denote the union of all I(u,v)for u,v∈S.The geodetic number g(G)of a graph G is the minimum cardinality of a set S with I(S)=V(G).For a digraph D,there is analogous terminology for the geodetic number g(D).The geodetic spectrum of a graph G,denoted by S(G),is the set of geodetic numbers of all orientations of graph G.The lower geodetic number is g~-(G)=minS(G)and the upper geodetic number is g~ (G)=maxS(G).The main purpose of this paper is to study the relations among g(G),g~-(G)and g~ (G)for connected graphs G.In addition,a sufficient and necessary condition for the equality of g(G)and g(G×K_2)is presented,which improves a result of Chartrand,Harary and Zhang. 相似文献
13.
Hong Lin Xiao-feng Guo 《应用数学学报(英文版)》2007,23(1):155-160
Let φ(G),κ(G),α(G),χ(G),cl(G),diam(G)denote the number of perfect matchings,connectivity,independence number,chromatic number,clique number and diameter of a graph G,respectively.In this note,by constructing some extremal graphs,the following extremal problems are solved:1.max{φ(G):|V(G)|=2n,κ(G)≤k}=k[(2n-3)!!],2.max{φ(G):|V(G)|=2n,α(G)≥k}=[multiply from i=0 to k-1(2n-k-i)[(2n-2k-1)!!],3.max{φ(G):|V(G)|=2n,χ(G)≤k}=φ(T_(k,2n))T_(k,2n)is the Turán graph,that is a complete k-partite graphon 2n vertices in which all parts are as equal in size as possible,4.max{φ(G):|V(G)|=2n,cl(G)=2}=n1,5.max{φ(G):|V(G)|=2n,diam(G)≥2}=(2n-2)(2n-3)[(2n-5)!!],max{φ(G):|V(G)|=2n,diam(G)≥3}=(n-1)~2[(2n-5)!!]. 相似文献
14.
A graph is point determining if distinct vertices have distinct neighborhoods. The nucleus of a point-determining graph is the set GO of all vertices, v, such that G–v is point determining. In this paper we show that the size, ω(G), of a maximum clique in G satisfies ω(G) ? 2|π (G)O|, where π(G) (the point determinant of G) is obtained from G by identifying vertices which have the same neighborhood. 相似文献
15.
Michael Reid 《Graphs and Combinatorics》1996,12(1):295-303
For a number fieldK
, consider the graphG(Kd), whose vertices are elements ofK
d, with an edge between any two points at (Euclidean) distance 1. We show thatG(K2) is not connected whileG(Kd) is connected ford 5. We also give necessary and sufficient conditions for the connectedness ofG(K3) andG(K4). 相似文献
16.
Fabrice Krieger 《Israel Journal of Mathematics》2009,172(1):425-444
Let G be a countable amenable group and P a polyhedron. The mean topological dimension mdim(X,G) of a subshift X ⊂ P
G
is a real number satisfying 0 ≤ mdim(X,G) ≤ dim(P), where dim(P) denotes the usual topological dimension of P. We give a construction of minimal subshifts X ⊂ P
G
with mean topological dimension arbitrarily close to dim(P). 相似文献
17.
Let γ(G) and i(G) be the domination number and independent domination number of a graph G, respectively. Sumner and Moore [8] define a graph G to be domination perfect if γ(H) = i(H), for every induced subgraph H of G. In this article, we give a finite forbidden induced subgraph characterization of domination perfect graphs. Bollobás and Cockayne [4] proved an inequality relating γ(G) and i(G) for the class of K1,k -free graphs. It is shown that the same inequality holds for a wider class of graphs. 相似文献
18.
A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful permutation representation of G is denoted by p(G). The minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers are denoted by q(G) and c(G) respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper p(G), q(G), c(G) and r(G) are calculated for the groups PSU (3, q2) and SU (3, q2).AMS Subject Classification (2000): 20C15 相似文献
19.
Given a graph G with n vertices and stability number α(G), Turán's Theorem gives a lower bound on the number of edges in G. Furthermore, Turán has proved that the lower bound is only attained if G is the union of α(G) disjoint balanced cliques. We prove a similar result for the 2-stability number α2(G) of G, which is defined as the largest number of vertices in a 2-colorable subgraph of G. Given a graph G with n vertices and 2-stability number α2(G), we give a lower bound on the number of edges in G and characterize the graphs for which this bound is attained. These graphs are the union of isolated vertices and disjoint
balanced cliques. We then derive lower bounds on the 2-stability number, and finally discuss the extension of Turán's Theorem
to the q-stability number, for q>2.
Received: July 21, 1999 Final version received: August 22, 2000
Present address: GERAD, 3000 ch. de la Cote-Ste-Catherine, Montreal, Quebec H3T 2A7, Canada. e-mail: Alain.Hertz@gerad.ca 相似文献
20.
Let G be a locally compact group with a weight function ω. Recently, we have shown that the Banach space L0∞ (G,1/ω) can be identified with the strong dual of L1(G, ω)equipped with some locally convex topologies τ. Here we use this duality to introduce an Arens multiplication on (L1(G, ω), τ)**, and prove that the topological center of (L1(G, ω), τ)** is (L1(G, ω); this enables us to conclude that (L1(G, ω), τ) is Arens regular if and only if G is discrete. We also give a characterization for Arens regularity of L0∞ (G, 1/ω)1.
Received: 8 March 2005 相似文献