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On the Dichromatic Number of Surfaces
In this paper, we give bounds on the dichromatic number $$\overrightarrow{\chi...
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On the Minimum Number of Arcs in 4-Dicritical Oriented Graphs
We prove that every 4-dicritical oriented graph on n vertices has at least...
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Decomposing and Colouring Locally Out-Transitive Oriented Graphs
We study the dichromatic number of a digraph, defined as the minimum number of parts in a partition of its vertex set into acyclic induced...
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The Potts Model, the Jones Polynomial and Link Homology
In the paper we explore how the Potts model in statistical mechanics is related to the Temperley-Lieb algebra, the Jones polynomial and Khovanov...
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Critical Graphs with few Edges
This chapter is concerned with the minimum number ext(k,n) of edges in k-critical graphswith n vertices. Brooks’ theorem says that 2ext(k,n) ≥ (k...
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The Chromatic Polynomial of a Digraph
An acyclic coloring of a digraph as defined by V. Neumann-Lara is a vertex-coloring such that no monochromatic directed cycles occur. Counting the...
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Edge colourings and qualitative representations of chromatic algebras
Conventional Ramsey-theoretic investigations for edge-colourings of complete graphs are framed around avoidance of certain configurations. Motivated...
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Colorings and Orientations of Graphs
Colorings and orientations of graphs are related in different ways, but the deepness of these relations is notwell understood. In this chapter we...
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Properties of Critical Graphs
In this chapterwe shall continue the study of critical graphs.Critical graphswere first introduced and investigated by G. A. Dirac in his doctoral...
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Relation of knot theories in some 3-manifolds to planar 1-polar knot diagrams
We relate equivalences of loops and arcs in some three manifolds to equivalences of various kinds of 1-polar knot diagrams on some subsets of a...
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From Knot Invariants to Knot Dynamics
This paper is an introduction to combinatorial topology via state summation models for the Jones polynomial and its generalizations and also an...
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Helmholtz and the geometry of color space: gestation and development of Helmholtz’s line element
Modern color science finds its birth in the middle of the nineteenth century. Among the chief architects of the new color theory, the name of the...
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On Inducing Degenerate Sums Through 2-Labellings
We deal with a variant of the 1–2–3 Conjecture introduced by Gao, Wang, and Wu (Graphs Combin 32:1415–1421, 2016) . This variant asks whether all...
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From Friezes to Quasicrystals: A History of Symmetry Groups
Even if, since many thousands of years, humans were fascinated by symmetry, which is reflected in many preserved ornaments on buildings, paintings,...
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From Friezes to Quasicrystals: A History of Symmetry Groups
Even if, since many thousands of years, humans were fascinated by symmetry, which is reflected in many preserved ornaments on buildings, paintings,...
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Dynamic Resource Allocation Networks in Marketing: Comparing the Effectiveness of Control Methods
The discrete- and continuous-time network models of opinions control and resource allocation in marketing are considered. Three cases of interaction...
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Coloring of Hypergraphs
Hypergraphs are discrete structures that generalize graphs in a very natural way. While in a graph every edge is incident with exactly two vertices,...