Problems Related to Graph Packing

Project: Research project

Description

The theory of graph packing provides a general framework for organizing many areas of graph theory. Two famous results that can be phrased in this language are Diracs Theorem on the existence of Hamiltonian cycles and the Hajnal-Szemredi Theorem on equitable coloring. Both are special cases of another important graph packing problem known as Seymours Conjecture. This conjecture has been proved for extremely large graphs by Komls, Srkzy and Szemerdi using their own Blow-Up Lemma and Szemerdis Regularity Lemma, but is still open for ordinary sized graphs. A final example is the Bollobs-Eldridge-Catalin Graph Packing Conjecture, for which only very special cases have been solved. Each of these problems requests a packing of certain graphs with bounded maximal degree. Many versions and special cases of these problems have been investigated by researches hoping to gain insight into the Graph Packing Conjecture, as well as other areas of graph theory. So far these efforts have met with only partial success. The principle investigator will work to advance these investigations, paying particular attention to variations in which the maximum degree condition is replaced by a weaker condition such as maximum Ore-degree, coloring number, or two coloring number. Algorithmic considerations related to packing
StatusFinished
Effective start/end date6/15/095/31/12

Funding

  • National Science Foundation (NSF): $287,040.00

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Graph Packing
Graph theory
Packing
Colouring
Graph in graph theory
Equitable Coloring
Regularity Lemma
Degree Condition
Packing Problem
Hamiltonian circuit
Maximum Degree
Theorem
Blow-up
Paul Adrien Maurice Dirac
Lemma
Partial