A hypergraph is d-degenerate if every subhypergraph has a vertex of degree at most d. A greedy algorithm colours every such hypergraph with at most d+ 1 colours. We show that this bound is tight, by constructing an r-uniform d-degenerate hypergraph with chromatic number d + 1 for all r ≥ 2 and d ≥ 1. Moreover, the hypergraph is triangle-free, where a triangle in an r-uniform hypergraph consists...

Edge contraction is shown to be a useful mechanism to improve lower bound heuristics for treewidth. A successful lower bound for treewidth is the degeneracy: the maximum over all subgraphs of the minimum degree. The degeneracy is polynomial time computable. We introduce the notion of contraction degeneracy: the maximum over all minors of the minimum degree. We show that the contraction degenera...

We prove an inequality involving the degeneracy, the cutwidth and the sparsity of graphs. It implies a quadratic lower bound on the cutwidth in terms of the degeneracy for all graphs and an improvement of it for clique-free graphs.

We quantify the observation by Kender and Freudenstein [24] that degenerate views occupy a significant fraction of the viewing sphere surrounding an object. For a perspective camera geometry, we introduce a computational model that can be used to estimate the probability that a view degeneracy will occur in a random view of a polyhedral object. For a typical recognition system parameterization,...

In this article, we study the degenerate periodic logistic equation with homogeneous Neumann boundary conditions:    ∂tu−∆u = au− b(x, t)u in Ω× (0,∞), ∂νu = 0 on ∂Ω× (0,∞), u(x, 0) = u0(x) ≥, 6≡ 0 in Ω, where Ω ⊂ R (N ≥ 2) is a bounded domain with smooth boundary ∂Ω, a and p > 1 are constants. The function b ∈ C(Ω × R) (0 < θ < 1) is T-periodic in t, nonnegative, and vanishes (i.e., has a...

Suppose M ≡ N . Recently, there has been much interest in the classification of groups. We show that ‖π‖ > ∅. In [31], the authors address the structure of manifolds under the additional assumption that xΩ = πV . Therefore in [31], the main result was the classification of non-elliptic monoids.

It has been argued that the power spectrum of the anisotropies in the Cosmic Microwave Background (CMB) may be effectively degenerate, namely that the observable spectrum does not determine a unique set of cosmological parameters. We describe the physical origin of this degeneracy and show that at small angular scales it is broken by gravitational lensing: effectively degenerate spectra become ...

As for a generic parameter dependent hamiltonian with the time reversal (TR) invariance, a non Abelian Berry connection with the Kramers (KR) degeneracy are introduced by using a quaternionic Berry connection. This quaternionic structure naturally extends to the many body system with the KR degeneracy. Its topological structure is explicitly discussed in comparison with the one without the KR d...

There is an evolutionary advantage in having multiple components with overlapping functionality (i.e degeneracy) in organisms. While theoretical considerations of degeneracy have been well established in neural networks using information theory, the same concepts have not been developed for differential systems, which form the basis of many biochemical reaction network descriptions in systems b...