2,074 research outputs found
The 4-girth-thickness of the complete multipartite graph
The -girth-thickness of a graph is the smallest number
of planar subgraphs of girth at least whose union is . In this paper, we
calculate the -girth-thickness of the complete -partite
graph when each part has an even number of vertices.Comment: 6 pages, 1 figur
Defective and Clustered Graph Colouring
Consider the following two ways to colour the vertices of a graph where the
requirement that adjacent vertices get distinct colours is relaxed. A colouring
has "defect" if each monochromatic component has maximum degree at most
. A colouring has "clustering" if each monochromatic component has at
most vertices. This paper surveys research on these types of colourings,
where the first priority is to minimise the number of colours, with small
defect or small clustering as a secondary goal. List colouring variants are
also considered. The following graph classes are studied: outerplanar graphs,
planar graphs, graphs embeddable in surfaces, graphs with given maximum degree,
graphs with given maximum average degree, graphs excluding a given subgraph,
graphs with linear crossing number, linklessly or knotlessly embeddable graphs,
graphs with given Colin de Verdi\`ere parameter, graphs with given
circumference, graphs excluding a fixed graph as an immersion, graphs with
given thickness, graphs with given stack- or queue-number, graphs excluding
as a minor, graphs excluding as a minor, and graphs excluding
an arbitrary graph as a minor. Several open problems are discussed.Comment: This is a preliminary version of a dynamic survey to be published in
the Electronic Journal of Combinatoric
Authentication in Welded Clad Plate with Similar Material and Thickness
This paper continues the research previously done by authors on numerical modelling of the dissimilar welded joints with varying clad thicknesses using a commercial finite element software. The current study simulates the welding conditions of a similar clad plate with a thin thickness. The computer simulated outcome then verified with the measured data of from other researchers. A close match between the numerical models and the experimental data was found.Peer reviewedFinal Published versio
A sixteen-relator presentation of an infinite hyperbolic Kazhdan group
We provide an explicit presentation of an infinite hyperbolic Kazhdan group
with generators and relators of length at most . That group acts
properly and cocompactly on a hyperbolic triangle building of type .
We also point out a variation of the construction that yields examples of
lattices in -buildings admitting non-Desarguesian residues of
arbitrary prime power order.Comment: 9 pages, 1 figur
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