Some results on the reconstruction problems. p‐claw‐free, chordal, and p4‐reducible graphs
Bhalchandra D. Thatte · Journal of Graph Theory · 1995
Abstract A claw is an induced subgraph isomorphic to K1,3. 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.