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Title of Journal: Graphs and Combinatorics

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Abbravation: Graphs and Combinatorics

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Springer Japan

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DOI

10.1002/sd.301

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1435-5914

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Bipartite Divisor Graphs for Integer Subsets

Authors: Mohammad A Iranmanesh Cheryl E Praeger
Publish Date: 2010/02/18
Volume: 26, Issue: 1, Pages: 95-105
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Abstract

Inspired by connections described in a recent paper by Mark L Lewis between the common divisor graph ΓX and the prime vertex graph ΔX for a set X of positive integers we define the bipartite divisor graph BX and show that many of these connections flow naturally from properties of BX In particular we establish links between parameters of these three graphs such as number and diameter of components and we characterise bipartite graphs that can arise as BX for some X Also we obtain necessary and sufficient conditions in terms of subconfigurations of BX for one of ΓX or ΔX to contain a complete subgraph of size 3 or 4

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  2. Exponentially Many Monochromatic n -Matchings in K 3 n -1
  3. Cubic Bridgeless Graphs and Braces
  4. The Linear Arboricity of Planar Graphs without 5-, 6-Cycles with Chords
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  10. Monochromatic Solutions for Multi-Term Unknowns
  11. Collapsible Graphs and Hamiltonicity of Line Graphs
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  16. Monitoring the Plane with Rotating Radars
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  18. The Interchange Graphs of Tournaments with Minimum Score Vectors Are Exactly Hypercubes
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