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Tree-Partitions with Bounded Degree Trees
A tree-partition of a graph G is a partition of V(G) such that identifying the vertices in each part gives a tree. It is known that every graph with...
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Uniform Degree
The distribution of a finite number of points in a polygon is referred to as a pattern in this book. Aggregation and uniformity are two typical...
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Calabi–Yau operators of degree two
We show that the solutions to the equations, defining the so-called Calabi–Yau condition for fourth-order operators of degree two, define a variety...
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Brouwer Degree The Core of Nonlinear Analysis
This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The...
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Characters of prime power degree in principal blocks
We describe finite groups whose principal block contains only characters of prime power degree.
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On the degree of global smoothings for subanalytic sets
In Bierstone and Parusiński (Duke Math J 167(16):3115–3128, 2018) proved the existence of global smoothings for closed subanalytic sets, both in an...
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The Brouwer Degree
The topological degree is a useful tool in the study of existence of solutions to nonlinear equations. In this chapter, we will study the finite...
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Theory of Topological Degree in Cones and Applications
The theory of topological degree in finite dimensional as well as Banach spaces has been discussed in detail in many monographs. In this chapter, we...
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PI degree of quantized Weyl algebras
In this article, the polynomial identity (PI) degree of the multiparameter quantized Weyl algebras have been explicitly computed at roots of unity.
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Degree Bounds for the Chromatic Number
Until the 1940s, coloring theory focused almost exclusively on coloring of maps. However, already in 1879 A. B. Kempe suggested coloring of abstract...
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Halin’s end degree conjecture
An end of a graph G is an equivalence class of rays, where two rays are equivalent if there are infinitely many vertex-disjoint paths between them in G ...
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Shadow Ratio of Hypergraphs with Bounded Degree
We study the size of the shadow of k -uniform hypergraphs with bounded degree. Lower bounds on the ratio of the size of the shadow and the size of the...
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Primes of higher degree and annihilators of class groups
Let L / K be a Galois extension of number fields with Galois group G . We discuss a new method, by studying primes of higher residue degree, to obtain...
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Approximate Sampling of Graphs with Near-P-Stable Degree Intervals
The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science,...
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Panconnectivity in Bipartite Graphs with Large Degree sum
In 1995, Amar et al. introduced the concept of panconnectivity for balanced bipartite graphs, and obtained a degree sum condition. In 2018, Du et...
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Structure of the Variety of Alternative Algebras with the Lie-Nilpotency Identity of Degree 5
We construct an additive basis for a relatively free alternative algebra of Lie-nilpotent degree 5, describe the associative center and core of this...