Some results on the reconstruction problems. p-claw-free,chordal, and p4-reducible graphs

A claw is an induced subgraph isomorphic to K_1,3. 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 P₄-reducible graphs is also presented. © 1995 John Wiley & Sons, Inc.