Thatte, BD (1994) Some results and approaches for reconstruction conjectures. In: Discrete Mathematics, 124 (1-3). 193-216 .
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Tutte (1979) proved that the disconnected spanning subgraphs of a graph can be reconstructed from its vertex deck. This result is used to prove that if we can reconstruct a set of connected graphs from the shuffled edge deck (SED) then the vertex reconstruction conjecture is true. It is proved that a set of connected graphs can be reconstructed from the SED when all the graphs in the set are claw-free or all are P-4-free. Such a problem is also solved for a large subclass of the class of chordal graphs. This subclass contains maximal outerplanar graphs. Finally, two new conjectures, which imply the edge reconstruction conjecture, are presented. Conjecture 1 demands a construction of a stronger k-edge hypomorphism (to be defined later) from the edge hypomorphism. It is well known that the Nash-Williams' theorem applies to a variety of structures. To prove Conjecture 2, we need to incorporate more graph theoretic information in the Nash-Williams' theorem.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier science.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||13 Apr 2011 08:49|
|Last Modified:||13 Apr 2011 08:49|
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