论文信息 - Notes on growing a tree in a graph

Notes on growing a tree in a graph

We study the height of a spanning tree $T$ of a graph $G$ obtained by starting with a single vertex of $G$ and repeatedly selecting, uniformly at random, an edge of $G$ with exactly one endpoint in $T$ and adding this edge to $T$.

[1] Arie M. C. A. Koster,et al. A Note on Contraction Degeneracy , 2004 .

[2] Carsten Thomassen,et al. Graphs on Surfaces , 2001, Johns Hopkins series in the mathematical sciences.

[3] Gábor Lugosi,et al. Concentration Inequalities - A Nonasymptotic Theory of Independence , 2013, Concentration Inequalities.

[4] Yoshiharu Kohayakawa,et al. On Richardsons model on the hypercube , 1997 .

[5] Luc Devroye,et al. Branching processes in the analysis of the heights of trees , 1987, Acta Informatica.

[6] Jack Hanson,et al. 50 years of first passage percolation , 2015, 1511.03262.

[7] M. Habib. Probabilistic methods for algorithmic discrete mathematics , 1998 .

[8] Béla Bollobás,et al. The Isoperimetric Number of Random Regular Graphs , 1988, Eur. J. Comb..

[9] James Allen Fill,et al. PERCOLATION, FIRST-PASSAGE PERCOLATION, AND COVERING TIMES FOR RICHARDSON'S MODEL ON THE n-CUBE (Short title: PERCOLATION ON THE CUBE) , 1993 .

[10] Unoriented first-passage percolation on the n-cube , 2014, 1402.2928.

[11] S. Janson. Tail bounds for sums of geometric and exponential variables , 2017, 1709.08157.

[12] Rick Durrett,et al. STOCHASTIC GROWTH MODELS: RECENT RESULTS AND OPEN PROBLEMS , 1989 .

[13] Boris G. Pittel,et al. Note on the Heights of Random Recursive Trees and Random m-ary Search Trees , 1994, Random Struct. Algorithms.