arXiv subjects

Sergey Ivanov

Publications and source records attributed to Sergey Ivanov.

3 recordsLinked to original sources

arXiv2026

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 shows that two can be necessary; some maximal planar graphs are already identified by one card. The argument exploits the fact that deleting a flippable edge leaves a single quadrilateral whose two diagonals give the only possible maximal-planar completions. Degree information then rules out the competing completion, with a separate argument for graphs containing a vertex of degree three. This settles a problem posed in a 2010 survey on reconstruction numbers.

math.CO↗

arXiv2026

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 pseudosimilar at the moment of deletion? We define the pseudosimilarity depth of a graph and construct connected graphs in which this process continues through all but a sublinear number of vertices. A two-clock construction gives a square-root deficit uniformly in the order, while a Chinese-remainder construction with many cyclic clocks yields an infinite family of asymmetric graphs with only a polylogarithmic number of vertices left outside the active chain. The mechanism realizes pseudosimilarity by breaking a long hidden automorphism orbit and enlarging the break one vertex at a time. Thus pseudosimilarity can persist through an asymptotically full sequence of vertex deletions, even though every graph encountered in the main construction is asymmetric.

math.CO↗

arXiv2026

Cost-Effective Repository Exploration for Agentic Issue Localization

Repository exploration is a distinct and costly stage of coding-agent pipelines: before generating a patch, an agent must identify which repository files are likely to matter. We study whether this stage can be delegated to lower-cost models while retaining useful localization quality. Using our IssueLoc-Bench, we evaluate five explorer models under the same read-only interactive interface on 499 SWE-bench Verified-derived tasks and 500 tasks from 153 additional repositories. We measure early candidate discovery, top-three gold-file coverage, strict file-set recovery, agent time, and token usage, with paired instance-level uncertainty and repository-clustered sensitivity analysis. The highest-quality explorer leads across localization metrics, but substantially cheaper operating points emerge: depending on the model and evaluation arm, lower-cost explorers retain approximately 78-94% of the reference Hit@3 and 73-92% of its F1 while reducing mean agent time by 41-88% and token usage by 84-95%. The preferred operating point depends on how localization is consumed downstream: ranking and coverage metrics characterize recoverable candidate handoffs, whereas F1 and exact match characterize restrictive file gates. These results support treating repository exploration as an independently measurable and budgetable stage of modular coding agents, with explorer selection guided by the downstream handoff contract.

cs.SE↗