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math.CO2026
The Class Edge-Reconstruction Number of a Maximal Planar Graph Is One or Two
Sergey Ivanov
An edge card of a graph is obtained by deleting one edge, and a class edge-reconstruction number asks for the fewest carefully selected cards that identify the graph when its class…
math.CO2026
Graphs with Long Pseudosimilarity Chains under Consecutive Vertex Deletions
Sergey Ivanov
Pseudosimilar vertices are vertices in distinct automorphism orbits whose deletions produce isomorphic graphs. Classical work has studied the existence, group-theoretic origin, and…
math.CO2026
Nonisomorphic Graphs Can Share an Arbitrarily Large Fraction of Their Vertex-Deleted Cards
Sergey Ivanov
For a graph , its vertex deck is the multiset of graphs obtained by deleting one vertex. Bowler, Brown, and Fenner (BBF) proposed as the maximum possibl…