论文信息 - The Minimal Spanning Tree in a Complete Graph and a Functional Limit Theorem for Trees in a Random Graph

The Minimal Spanning Tree in a Complete Graph and a Functional Limit Theorem for Trees in a Random Graph

The minimal weight of a spanning tree in a complete graph Kn with independent, uniformly distributed random weights on the edges is shown to have an asymptotic normal distribution. The proof uses a functional limit extension of results by Barbour and Pittel on the distribution of the number of tree components of given sizes in a random graph.

Svante Janson | S. Janson

[1] Alan M. Frieze,et al. On the value of a random minimum spanning tree problem , 1985, Discret. Appl. Math..

[2] N. H. Abel. Beweis eines Ausdruckes, von welchem die Binomial-Formel ein einzelner Fall ist. , 1826 .

[3] Svante Janson. Multicyclic Components in a Random Graph Process , 1993, Random Struct. Algorithms.

[4] M. Kruskal,et al. The Expected Number of Components Under a Random Mapping Function , 1954 .

[5] A. Barbour. Poisson convergence and random graphs , 1982 .

[6] Boris G. Pittel,et al. On Tree Census and the Giant Component in Sparse Random Graphs , 1990, Random Struct. Algorithms.

[7] Robert E. Tarjan,et al. A Linear-Time Algorithm for Finding a Minimum Spanning Pseudoforest , 1988, Inf. Process. Lett..

[8] S. Janson. Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics , 1994 .