Edge Reconstruction Conjecture

Importance: High ✭✭✭
Author(s): Harary, Frank
Subject: Graph Theory
Keywords: reconstruction
Recomm. for undergrads: no
Posted by: melch
on: May 23rd, 2008

\begin{conjecture} % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. Every simple graph with at least 4 edges is reconstructible from it's edge deleted subgraphs \end{conjecture}

% You may use many features of TeX, such as % arbitrary math (between $...$ and $$...$$) % \begin{theorem}...\end{theorem} environment, also works for question, problem, conjecture, ... % % Our special features: % Links to wikipedia: \Def {mathematics} or \Def[coloring]{Graph_coloring} % General web links: \href [The On-Line Encyclopedia of Integer Sequences]{http://www.research.att.com/~njas/sequences/}

It is known that if a graph is vertex reconstructible then it is edge reconstructible.


% Example: %*[B] Claude Berge, Farbung von Graphen, deren samtliche bzw. deren ungerade Kreise starr sind, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10 (1961), 114. % %[CRS] Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas: \arxiv[The strong perfect graph theorem]{math.CO/0212070}, % Ann. of Math. (2) 164 (2006), no. 1, 51--229. \MRhref{MR2233847} % % (Put an empty line between individual entries)

J.A.Bondy, A graph reconstruction manual, Surveys in Combinatorics, LMS-Lecture Note Series 166(1991)

* indicates original appearance(s) of problem.