# Counting shellings of complete bipartite graphs and trees

```@article{Gao2018CountingSO,
title={Counting shellings of complete bipartite graphs and trees},
author={Yibo Gao and Junyao Peng},
journal={Journal of Algebraic Combinatorics},
year={2018},
volume={54},
pages={17 - 37}
}```
• Published 26 September 2018
• Mathematics
• Journal of Algebraic Combinatorics
A shelling of a graph, viewed as an abstract simplicial complex that is pure of dimension 1, is an ordering of its edges such that every edge is adjacent to some other edges appeared previously. In this paper, we focus on complete bipartite graphs and trees. For complete bipartite graphs, we obtain an exact formula for their shelling numbers. And for trees, we relate their shelling numbers to linear extensions of tree posets and bound shelling numbers using vertex degrees and diameter.

## References

SHOWING 1-10 OF 15 REFERENCES

• Mathematics
SoCG
• 2018
We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978.
• Mathematics
J. Comb. Theory, Ser. A
• 1989
• Mathematics
• 2011
Björner and Wachs provided two q-generalizations of Knuth’s hook formula counting linear extensions of forests: one involving the major index statistic, and one involving the inversion number
• D. Kozlov
• Mathematics
Algorithms and computation in mathematics
• 2008
Concepts of Algebraic Topology, Applications of Spectral Sequences to Hom Complexes, and Structural Theory of Morphism Complexes are presented.
The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Usually are given an infinite class of finite sets S i where i ranges over some index set I
• Mathematics
• 1988
For (W, S) a Coxeter group, we study sets of the form W/V = {w E W I l(wv) = 1(w) + I(v) for all v E V}, where V C W. Such sets W/V, here called generalized quotients, are shown to have much of the
• Art
• 2001
Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on.
Based on a graduate course given at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward