Media type: E-Article Title: Some results on the reconstruction problems. p‐claw‐free, chordal, and p4‐reducible graphs Contributor: Thatte, Bhalchandra D. imprint: Wiley, 1995 Published in: Journal of Graph Theory Language: English DOI: 10.1002/jgt.3190190409 ISSN: 0364-9024; 1097-0118 Keywords: Geometry and Topology ; Discrete Mathematics and Combinatorics Origination: Footnote: Description: <jats:title>Abstract</jats:title><jats:p>A claw is an induced subgraph isomorphic to K<jats:sub>1,3.</jats:sub> The claw‐point is the point of degree 3 in a claw. A graph is called p‐claw‐free when no p‐cycle has a claw‐point on it. It is proved that for p ≥ 4, p‐claw‐free graphs containting at least one chordless p‐cycle are edge reconstructible. It is also proved that chordal graphs are edge reconstructible. These two results together imply the edge reconstructibility of claw‐free graphs. A simple proof of vertex reconstructibility of P<jats:sub>4</jats:sub>‐reducible graphs is also presented. © 1995 John Wiley & Sons, Inc.</jats:p>