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101.
102.
Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false. 相似文献
103.
104.
If sk denotes the number of independent sets of cardinality k and α(G) is the size of a maximum independent set in graph G, then I(G;x)=s0+s1x+?+sα(G)xα(G) is the independence polynomial of G (Gutman and Harary, 1983) [8].In this paper we provide an elementary proof of the inequality|I(G;−1)|≤2φ(G) (Engström, 2009) [7], where φ(G) is the decycling number of G (Beineke and Vandell, 1997) [3], namely, the minimum number of vertices that have to be deleted in order to turn G into a forest. 相似文献
105.
In this note, we present a correction of Theorem 2 in the paper [1], and show that all the conditions (I1)–(I5) in the definition of fuzzy implication algebras are independent of each other. In addition, we prove that the class of all commutative fuzzy implication algebras forms an equational algebra class. 相似文献
106.
For a set of vertices of a graph , a vertex in , and a vertex in , let be the distance of and in the graph . Dankelmann et al. (2009) define to be an exponential dominating set of if for every vertex in , where . Inspired by this notion, we define to be an exponential independent set of if for every vertex in , and the exponential independence number of as the maximum order of an exponential independent set of .Similarly as for exponential domination, the non-local nature of exponential independence leads to many interesting effects and challenges. Our results comprise exact values for special graphs as well as tight bounds and the corresponding extremal graphs. Furthermore, we characterize all graphs for which equals the independence number for every induced subgraph of , and we give an explicit characterization of all trees with . 相似文献
107.
Marco Baioletti 《International Journal of Approximate Reasoning》2011,52(5):565-579
We deal with conditional independencies, which have a fundamental role in probability and multivariate statistics. The structure of probabilistic independencies is described by semigraphoids or, for strictly positive probabilities, by graphoids. In this paper, given a set of independencies compatible with a probability, the attention is focused toward the problem of computing efficiently the closure with respect to the semigraphoid and graphoid structures. We introduce a suitable notion of projection in order to provide a new method which properly uses conditional independence statements. 相似文献
108.
In 1968, Vizing conjectured that, if G is a Δ-critical graph with n vertices, then α(G)?n/2, where α(G) is the independence number of G. In this note, we verify this conjecture for n?2Δ. 相似文献
109.
This paper considers the independence test for two stationary infinite order autoregressive processes. For a test, we follow
the empirical process method and construct the Cramér-von Mises type test statistics based on the least squares residuals.
It is shown that the proposed test statistics behave asymptotically the same as those based on true errors. Simulation results
are provided for illustration. 相似文献
110.