Author

Sergey Ivanov

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Preprint Aug 2026

Graphs with Long Pseudosimilarity Chains under Consecutive Vertex Deletions

Pseudosimilar vertices are vertices in distinct automorphism orbits whose deletions produce isomorphic graphs. Classical work has studied the existence, group-theoretic origin, and construction of large sets of such vertices. We ask a different recursive question: how long can one repeatedly delete a vertex that is pse...

Sergey Ivanov · 1 citation

Review Sep 2026

The Class Edge-Reconstruction Number of a Maximal Planar Graph Is One or Two

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 is known. We determine the sharp universal bound for maximal planar graphs. Two selected cards always suffice, and the octahedral graph sho...

Sergey Ivanov · 0 citations

Preprint Aug 2026

Nonisomorphic Graphs Can Share an Arbitrarily Large Fraction of Their Vertex-Deleted Cards

For a graph $G$, its vertex deck is the multiset of graphs obtained by deleting one vertex. Bowler, Brown, and Fenner (BBF) proposed $2\lfloor(n-1)/3\rfloor$ as the maximum possible overlap between the decks of two nonisomorphic $n$-vertex graphs, for all sufficiently large $n$. We first give an explicit pair of connec...

Sergey Ivanov · 2 citations