David Rivshin

Abstract

First proposed in 1941 by Kelly and Ulam, the Graph Reconstruction Conjecture has been called the major open problem in the field of Graph Theory. While the Graph Reconstruction Conjecture is still unproven it has spawned a number of related questions. In the classical vertex graph reconstruction number problem a vertex is deleted in every possible way from a graph G, and then it can be asked how many (both minimum and maximum values) of these subgraphs are required to uniquely reconstruct G (up to isomorphism). This problem can then be extended to k-vertex deletion (for 1 ≤ k ≤ |V (G)|), and to k-edge deletion (for 1 ≤ k ≤ |E(G)|). For some classes of graphs there is known a formula to directly compute its reconstruction numbers. However, for the vast majority of graphs the computation devolves to brute force exhaustive search. Previous computer searches have computed the 1-vertex-deletion reconstruction numbers of all graphs of up to 10 vertices, as well as computing 2-vertex-deletion reconstructibility of all graphs on up to 9 vertices. In this project I have developed and implemented an improved algorithm to compute 1-vertex-deletion reconstruction numbers with an O(|V (G)|) speedup, allowing their computation for all graphs of up to 11 vertices. In addition the ability to compute arbitrary k-vertex and edge deletion reconstruction numbers has been implemented, leading to many new results in these areas.

Publication Date

2008

Document Type

Master's Project

Student Type

Graduate

Department, Program, or Center

Computer Science (GCCIS)

Advisor

Hemaspaandra, Edith

Advisor/Committee Member

Faliszewski, Piotr

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2013.

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DRivshinProposal2007.pdf (135 kB)

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RIT – Main Campus

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