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51.
We investigate the transfer of w-stability and Clifford w-regularity from a domain D to the polynomial ring D[X]. We show that these two properties pass from D to D[X] when D is either integrally closed or it is Mori and w-divisorial. 相似文献
52.
53.
Andrew Lyons 《Discrete Applied Mathematics》2011,159(16):1842-1850
An acyclic coloring of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of star coloring requires that the union of any two color classes induces a disjoint collection of stars. We prove that every acyclic coloring of a cograph is also a star coloring and give a linear-time algorithm for finding an optimal acyclic and star coloring of a cograph. If the graph is given in the form of a cotree, the algorithm runs in O(n) time. We also show that the acyclic chromatic number, the star chromatic number, the treewidth plus 1, and the pathwidth plus 1 are all equal for cographs. 相似文献
54.
赵长健 《数学年刊A辑(中文版)》2011,32(4):473-480
首次提出并建立了凸体的体积差函数的等周不等式,它是经典等周不等式的推广.作为应用,对星体建立了体积差函数的对偶等周不等式和广义对偶等周不等式. 相似文献
55.
Let A be a Hermitian matrix whose graph is G (i.e. there is an edge between the vertices i and j in G if and only if the (i,j) entry of A is non-zero). Let λ be an eigenvalue of A with multiplicity mA(λ). An edge e=ij is said to be Parter (resp., neutral, downer) for λ,A if mA(λ)−mA−e(λ) is negative (resp., 0, positive ), where A−e is the matrix resulting from making the (i,j) and (j,i) entries of A zero. For a tree T with adjacency matrix A a subset S of the edge set of G is called an edge star set for an eigenvalue λ of A, if |S|=mA(λ) and A−S has no eigenvalue λ. In this paper the existence of downer edges and edge star sets for non-zero eigenvalues of the adjacency matrix of a tree is proved. We prove that neutral edges always exist for eigenvalues of multiplicity more than 1. It is also proved that an edge e=uv is a downer edge for λ,A if and only if u and v are both downer vertices for λ,A; and e=uv is a neutral edge if u and v are neutral vertices. Among other results, it is shown that any edge star set for each eigenvalue of a tree is a matching. 相似文献
56.
Given an undirected graph, a star partition is a partition of the nodes into subsets with at least two nodes so that the subgraph induced by each subset has a spanning star. Star partitions are related to well-known problems concerning domination in graphs and edge covering. We focus on the Constrained Star Partition Problem (CSP) that asks for finding a star partition of given cardinality. The problem is new and presents interesting peculiarities. We explore the relation between the cardinalities of star partitions and domatic bipartitions, showing that there are star partitions of any cardinality between minimum and maximum values, and that a similar but weaker result holds for domatic bipartitions. We study the computational complexity of different versions of star partition and domatic bipartition problems, proving that most of them, in particular CSP, constrained domatic bipartition and balanced domatic bipartition, are NP-complete. We also show that star partition problems are polynomial on trees and, more generally, on bounded treewidth graphs. We introduce an integer linear programming formulation that defines a polytope containing all the star partitions of a graph, showing that its vertices have only integral components for trees, which implies that linear programming can be used to solve weighted star partition problems on trees. 相似文献
57.
58.
We give conditions under which an n-star module extends to an n-star module, or an n-tilting module, over a ring extension R of A. In case that R is a split extension of A by Q, we obtain that is a 1-tilting module (respectively, a 1-star module) if and only if is a 1-tilting module (respectively, a 1-star module) and generates both and (respectively, generates ), where is an injective cogenerator in the category of all left A-modules. These extend results in [I. Assem, N. Marmaridis, Tilting modules over split-by-nilpotent extensions, Comm. Algebra 26 (1998) 1547–1555; K.R. Fuller, *-Modules over ring extensions, Comm. Algebra 25 (1997) 2839–2860] by removing the restrictions on R and Q. 相似文献
59.
60.
De Ming Li 《数学学报(英文版)》2002,18(1):173-180
The notion of the star chromatic number of a graph is a generalization of the chromatic number. In this paper, we calculate
the star chromatic numbers of three infinite families of planar graphs. The first two families are derived from a 3-or 5-wheel
by subdivisions, their star chromatic numbers being 2+2/(2n + 1), 2+3/(3n + 1), and 2+3(3n−1), respectively. The third family of planar graphs are derived from n odd wheels by Hajos construction with star chromatic numbers 3 + 1/n, which is a generalization of one result of Gao et al.
Received September 21, 1998, Accepted April 9, 2001. 相似文献