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}
}
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

Shellability is NP-complete

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.

q-Hook length formulas for forests

A multivariate “inv” hook formula for forests

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

Combinatorial Algebraic Topology

  • 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.

Separable elements in Weyl groups

What Is Enumerative Combinatorics

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

Generalized quotients in Coxeter groups

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

The Art in Computer Programming

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.

Lectures on Polytopes

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