共查询到20条相似文献,搜索用时 46 毫秒
1.
Heinz Gröflin 《Combinatorica》1984,4(4):281-290
Given a digraphG = (V, E), call a node setT ⊆V path-closed ifv, v′ εT andw εV is on a path fromv tov′ impliesw εT. IfG is the comparability graph of a posetP, the path-closed sets ofG are the convex sets ofP. We characterize the convex hull of (the incidence vectors of) all path-closed sets ofG and its antiblocking polyhedron inR
v
, using lattice polyhedra, and give a minmax theorem on partitioning a given subset ofV into path-closed sets. We then derive good algorithms for the linear programs associated to the convex hull, solving the
problem of finding a path-closed set of maximum weight sum, and prove another min-max result closely resembling Dilworth’s
theorem. 相似文献
2.
Let G = (V, E) be a graph without isolated vertices. A set S lohtain in V is a domination set of G if every vertex in V - S is adjacent to a vertex in S, that is N[S] = V. The domination number of G, denoted by γ(G), is the minimum cardinality of a domination set of G. A set S lohtain in V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S] has a perfect matching. The paired-domination number, denoted by γpr(G), is defined to be the minimum cardinality of a paired-domination set S in G. A subset S lohtain in V is a power domination set of G if all vertices of V can be observed recursively by the following rules: (i) all vertices in N[S] are observed initially, and (ii) if an observed vertex u has all neighbors observed except one neighbor v, then v is observed (by u). The power domination number, denoted by γp(G), is the minimum cardinality of a power domination set of G. In this paper, the constructive characterizations for trees with γp=γ and γpr = γp are provided respectively. 相似文献
3.
Peter Dankelmann Johannes H. Hattingh Michael A. Henning Henda C. Swart 《Journal of Global Optimization》2006,34(4):597-607
Let G = (V,E) be a graph and let S V. The set S is a packing in G if the vertices of S are pairwise at distance at least three apart in G. The set S is a dominating set (DS) if every vertex in V − S is adjacent to a vertex in S. Further, if every vertex in V − S is also adjacent to a vertex in V − S, then S is a restrained dominating set (RDS). The domination number of G, denoted by γ(G), is the minimum cardinality of a DS of G, while the restrained domination number of G, denoted by γr(G), is the minimum cardinality of a RDS of G. The graph G is γ-excellent if every vertex of G belongs to some minimum DS of G. A constructive characterization of trees with equal domination and restrained domination numbers is presented. As a consequence
of this characterization we show that the following statements are equivalent: (i) T is a tree with γ(T)=γr(T); (ii) T is a γ-excellent tree and T ≠ K2; and (iii) T is a tree that has a unique maximum packing and this set is a dominating set of T. We show that if T is a tree of order n with ℓ leaves, then γr(T) ≤ (n + ℓ + 1)/2, and we characterize those trees achieving equality. 相似文献
4.
We prove that ifX is a Polish space andF a face ofP(X) with the Baire property, thenF is either a meager or a co-meager subset ofP(X). As a consequence we show that for every abelian Polish groupX and every analytic Haar-null set Λ⊆X, the set of test measuresT(Λ) of Λ is either meager or co-meager. We characterize the non-locally-compact groups as the ones for which there exists
a closed Haar-null setF⊆X withT(F) meager, Moreover, we answer negatively a question of J. Mycielski by showing that for every non-locally-compact abelian Polish
group and every σ-compact subgroupG ofX there exists aG-invariantF
σ subset ofX which is neither prevalent nor Haar-null.
Research supported by a grant of EPEAEK program “Pythagoras”. 相似文献
5.
WANGWEIFAN ZHANGKEMIN 《高校应用数学学报(英文版)》1997,12(4):455-462
A Planar graph g is called a ipseudo outerplanar graph if there is a subset v.∈V(G),[V.]=i,such that G-V. is an outerplanar graph in particular when G-V.is a forest ,g is called a i-pseudo-tree .in this paper.the following results are proved;(1)the conjecture on the total coloring is true for all 1-pseudo-outerplanar graphs;(2)X1(G) 1 fo any 1-pseudo outerplanar graph g with △(G)≥3,where x4(G)is the total chromatic number of a graph g. 相似文献
6.
Let ℱ be a class of groups and let G be a finite group. We call a set Σ of subgroups of G a covering subgroup system of G for ℱ (or directly an ℱ-covering subgroup system of G) if G ∈ ℱ whenever every subgroup in Σ is in ℱ. We give some covering subgroup systems for the class of all p-nilpotent groups. 相似文献
7.
Ladislav Nebeský 《Czechoslovak Mathematical Journal》2007,57(1):465-471
By a chordal graph is meant a graph with no induced cycle of length ⩾ 4. By a ternary system is meant an ordered pair (W, T), where W is a finite nonempty set, and T ⊆ W × W × W. Ternary systems satisfying certain axioms (A1)–(A5) are studied in this paper; note that these axioms can be formulated
in a language of the first-order logic. For every finite nonempty set W, a bijective mapping from the set of all connected chordal graphs G with V(G) = W onto the set of all ternary systems (W, T) satisfying the axioms (A1)–(A5) is found in this paper. 相似文献
8.
Stephen H. Hechler 《Israel Journal of Mathematics》1971,10(4):413-432
A family of infinite subsets of the setN of natural numbers will be called almost disjoint iff any two of its members have finite intersection. We shall define such
a family ℱ to ben-separable iff for every decompositionD = {D
1, …D
n
} ofN inton or fewer disjoint subsets there exist setsF ∈ ℱ andD ∃D such thatF ⊆D, and we shall use this and related notions to classify almost-disjoint families, using, on occasion, special axioms of set
theory. 相似文献
9.
Let G = (V, E) be a simple graph. A subset S ⊆ V is a dominating set of G, if for any vertex u ∈ V-S, there exists a vertex v ∈ S such that uv ∈ E. The domination number, denoted by γ(G), is the minimum cardinality of a dominating set. In this paper we will prove that if G is a 5-regular graph, then γ(G) ⩽ 5/14n. 相似文献
10.
Shirong Li 《中国科学A辑(英文版)》1998,41(11):1121-1127
The class ℱpc of all finite groupsG is defined such thatX≤G implies that there exists an ℱ-subnormal subgroupS ofG containingX such thatX is ℱ-subabnormal inS, where ℱ is a saturated formation, closed under taken subgroups. Groups in ℱpc are characterized by ℱ-projectors and ℱ-covering subgroups.
Project supported by the National Natural Science Foundation of China (Grant No. 19760001) and the Natural Science Foundation
of Guangxi Autonomous Region. 相似文献
11.
LetR be a ring, and let (ℐ, ℱ) be an hereditary torsion theory of leftR-modules. An epimorphism ψ:M→X is called a torsion-free cover ofX if (1)M∈ ℱ, (2) every homomorphism from a torsion-free module intoX can be factored throughM, and (3) ker ψ contains no nonzero ℐ -closed submodules ofM. Conditions onM andN are studied to determine when the natural mapsM→M/N andQ(M)→Q(M)/N are torsion-free covers, whenQ(M) is the localization ofM with respect to (ℐ, ℱ). IfM→M/N is a torsion-free cover andM is projective, thenN⊆radM. Consequently, the concepts of projective cover and torsion-free cover coincide in some interesting cases. 相似文献
12.
LetG be a group,ZG the integral group ring ofG andI(G) its augmentation ideal. Subgroups determined by certain ideals ofZG contained inI(G) are identified. For example, whenG=HK, whereH, K are normal subgroups ofG andH∩K⊆ζ(H), then the subgroups ofG determined byI(G)I(H)I(G), andI
3(G)I(H) are obtained. The subgroups of any groupG with normal subgroupH determined by (i)I
2(G)I(H)+I(G)I(H)I(G)+I(H)I2(G), whenH′⊆[H,G,G] and (ii)I(G)I(H)I(G) when degH
2(G/H′, T)≤1, are computed. the subgroup ofG determined byI
n(G)+I(G)I(H) whenH is a normal subgroup ofG withG/H free Abelian is also obtained 相似文献
13.
Bounds on the Distance Two-Domination Number of a Graph 总被引:1,自引:0,他引:1
For a graph G = (V, E), a subset D⊆V(G) is said to be distance two-dominating set in G if for each vertex u∈V−D, there exists a vertex v∈D such that d(u,v)≤2. The minimum cardinality of a distance two-dominating set in G is called a distance two-domination number and is denoted by γ2(G). In this note we obtain various upper bounds for γ2(G) and characterize the classes of graphs attaining these bounds.
Received: May 31, 1999 Final version received: July 13, 2000 相似文献
14.
Let G=(V,E) be a simple graph. A subset D⊆V is a dominating set of G, if for any vertex x ∈ V−D, there exists a vertex y ∈ D such that xy ∈ E. By using the so-called vertex disjoint paths cover introduced by Reed, in this paper we prove that every graph G on n vertices with minimum degree at least five has a dominating set of order at most 5n/14. 相似文献
15.
Summary Letℱ denote the convolution semigroup of probability distributions on the real line. We prove thatno element of ℱ is prime in the sense that given anℱ one can always find two distributionsG,H∈ℱ such thatF is a convolution factor ofG#x002A;H but neither ofG nor ofH. In contrast,ℱ is known to possess many irreducible elements. 相似文献
16.
Closed Separator Sets 总被引:1,自引:0,他引:1
Matthias Kriesell 《Combinatorica》2005,25(5):575-598
A smallest separator in a finite, simple, undirected graph G is a set S ⊆ V (G) such that G–S is disconnected and |S|=κ(G), where κ(G) denotes the connectivity of G.
A set S of smallest separators in G is defined to be closed if for every pair S,T ∈ S, every component C of G–S, and every component S of G–T intersecting C either X(C,D) := (V (C) ∩ T) ∪ (T ∩ S) ∪ (S ∩ V (D)) is in S or |X(C,D)| > κ(G). This leads, canonically, to a closure system on the (closed) set of all smallest separators of G.
A graph H with
is defined to be S-augmenting if no member of S is a smallest separator in G ∪ H:=(V (G) ∪ V (H), E(G) ∪ E(H)). It is proved that if S is closed then every minimally S-augmenting graph is a forest, which generalizes a result of Jordán.
Several applications are included, among them a generalization of a Theorem of Mader on disjoint fragments in critically k-connected graphs, a Theorem of Su on highly critically k-connected graphs, and an affirmative answer to a conjecture of Su on disjoint fragments in contraction critically k-connected graphs of maximal minimum degree. 相似文献
17.
A set A⊆V of the vertices of a graph G=(V,E) is an asteroidal set if for each vertex a∈A, the set A\{a} is contained in one component of G−N[a]. The maximum cardinality of an asteroidal set of G, denoted by an (G), is said to be the asteroidal number of G. We investigate structural properties of graphs of bounded asteroidal number. For every k≥1, an (G)≤k if and only if an (H)≤k for every minimal triangulation H of G. A dominating target is a set D of vertices such that D∪S is a dominating set of G for every set S such that G[D∪S] is connected. We show that every graph G has a dominating target with at most an (G) vertices. Finally, a connected graph G has a spanning tree T such that d
T
(x,y)−d
G
(x,y)≤3·|D|−1 for every pair x,y of vertices and every dominating target D of G.
Received: July 3, 1998 Final version received: August 10, 1999 相似文献
18.
Romeo Rizzi 《Graphs and Combinatorics》2000,16(3):355-358
Let Cone(G), Int.Cone(G) and Lat(G) be the cone, the integer cone and the lattice of the incidence vectors of the circuits of graph G. A good range is a set ?⊆ℕ such that Cone (G)∩Lat (G)∩?E⊆Int.Cone(G) for every graph G(V,E). We give a counterexample to a conjecture of Goddyn [1] stating that ℕ\{1} is a good range.
Received: November 26, 1997 相似文献
19.
Shi Rong Li 《数学学报(英文版)》2008,24(4):647-654
Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown: (1) G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; (2) G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F(H), the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G. 相似文献
20.
Günter Heimbeck 《Geometriae Dedicata》1987,22(2):235-245
Let K be any commutative field and V:=K
4. A collection
of ruled quadrics in V is called a flock of ruled quadrics if the following holds true. (1) ⋃ℱ∈
G
ℱ = V; (2) There is a line S⊂V such that ℱ1⋂ℱ2= S for all distinct ℱ1, ℱ2∈
. The group ΓL(V) decomposes the set of all those flocks into equivalence classes. Besides that, we consider any cone R in V, say R:= {x∈V|x
1
x
3 - x
2
2
= 0}. Let R denote the set of all regular points of R. Plane sections of R which do not contain the singular point of ℜ are called regular sections. We consider decompositions of R
* by regular sections and their equivalence classes with respect to the symmetry group ΓL(V)R of the cone ℜ. The main result is as follows. There is a (natural) bijection between the classes of equivalent flocks of
rules quadrics and the classes of equivalent decompositions of R
* by regular sections. A brief discussion of those flocks of ruled quadrics on which the construction of the so-called Betten-Walker
planes is based ends the paper. Provided that char K≠3, these planes exist if and only if x∈K→x
3∈K is bijective.
相似文献