{"total":11,"items":[{"citing_arxiv_id":"2605.11288","ref_index":19,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"On $2$-factors of Hamiltonian graphs","primary_cat":"math.CO","submitted_at":"2026-05-11T22:16:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Large Hamiltonian graphs with minimum degree n to the power 1 minus a small epsilon contain a 2-factor consisting of exactly k cycles.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.10941","ref_index":37,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity","primary_cat":"cs.CC","submitted_at":"2026-05-11T17:59:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Exponential lower bounds for cutting planes and Res(⊕) on binary clique formulas for random dense graphs, with polynomial randomized communication complexity for falsified clause finding.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"threshold value is Θ(n −2/(k−1)). We also define thek-partiteversion of the same distribution: For a fixed partition of the nodes, G(n, p, k) is sampled from by first samplingG∼ G(nk, p) and then intersectingGwith a complete k-partite graph withnnodes in each part. 2.2 Proof Complexity We next recall some basic notions from proof complexity; see, e.g., [37, 11] for a more thorough exposition. A Boolean variablexor its negation xis called aliteral, and a disjunction of literals over pairwise disjoint variablesC=ℓ 1 ∨ · · · ∨ℓk is called aclause. ACNF formulais a conjunction of clausesF=C 1 ∧ · · · ∧C m. We sometimes call the clauses ofFaxioms, and denote the set of variables occurring inFas Vars(F). Cutting Planes."},{"citing_arxiv_id":"2605.09821","ref_index":20,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Online Steiner Forest with Recourse","primary_cat":"cs.DS","submitted_at":"2026-05-10T23:54:46+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"An algorithm for online Steiner forest achieves constant competitiveness with amortized O(log n) recourse.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.08498","ref_index":33,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"MathConstraint: Automated Generation of Verified Combinatorial Reasoning Instances for LLMs","primary_cat":"cs.LG","submitted_at":"2026-05-08T21:28:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"MathConstraint generates scalable, automatically verifiable combinatorial problems where LLMs achieve 18.5-66.9% accuracy without tools but roughly double that with solver access.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"[31] Xia Jiang, Jing Chen, Cong Zhang, Jie Gao, Chengpeng Hu, Chenhao Zhang, Yaoxin Wu, and Yingqian Zhang. Reasoning in a combinatorial and constrained world: Benchmarking llms on natural-language combinatorial optimization.arXiv preprint arXiv:2602.02188, 2026. [32] Haocheng Ju and Bin Dong. Ai for mathematics: Progress, challenges, and prospects.arXiv preprint arXiv:2601.13209, 2026. [33] Richard M. Karp.Reducibility among Combinatorial Problems, pages 85-103. Springer US, Boston, MA, 1972. ISBN 978-1-4684-2001-2. doi: 10.1007/978-1-4684-2001-2_9. URL https://doi.org/10.1007/978-1-4684-2001-2_9. [34] Markus Kirchweger and Stefan Szeider. Sat modulo symmetries for graph generation. In27th International Conference on Principles and Practice of Constraint Programming (CP 2021),"},{"citing_arxiv_id":"2605.06123","ref_index":37,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Back to the Beginning of Heuristic Design: Bridging Code and Knowledge with LLMs","primary_cat":"cs.AI","submitted_at":"2026-05-07T12:30:58+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A knowledge-first approach to LLM-driven automatic heuristic design in combinatorial optimization yields better discovery efficiency, transfer, and generalization than code-centric baselines by formalizing a distortion-compression trade-off.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.06037","ref_index":22,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A virtually connected probabilistic computer as a solver for higher-order, densely connected, or reconfigurable combinatorial optimisation problems","primary_cat":"cs.AR","submitted_at":"2026-05-07T11:26:07+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Simulations predict that a virtually connected photonic probabilistic computer solves Erdos-Renyi graph spin-glass ground states orders of magnitude faster than digital annealing units by avoiding embedding and sparsification.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.01410","ref_index":17,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Facial diagrams and cycle double cover","primary_cat":"math.CO","submitted_at":"2026-05-02T12:13:31+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Studying twists of edges in embeddings of cubic graphs yields bounds on the number of singular edges.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.24237","ref_index":5,"ref_count":2,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Computational Complexity of the Interval Ordering Problem","primary_cat":"cs.DS","submitted_at":"2026-04-27T09:46:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Dynamic programming solves interval ordering in O(2^n poly(n)) time via oracle access to f, in polynomial time when f-f(0) is subadditive or superadditive, with a 2^{n-1} lower bound and NP-hardness for some simple f.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.20589","ref_index":41,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"The Mihail-Vazirani conjecture and strong edge-expansion in random $0/1$ polytopes","primary_cat":"math.CO","submitted_at":"2026-04-22T14:08:16+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Random 0/1 polytopes have edge-expansion Θ(d) whp for p ≤ 1-ε and Ω(d^k) for any k when p ≤ 1/2-ε, verifying the Mihail-Vazirani conjecture in strong form with a phase transition at p=1/2.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.10828","ref_index":20,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Maximum Independent Sets in Disk Graphs with Disks in Convex Position","primary_cat":"cs.CG","submitted_at":"2026-04-12T21:49:26+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"O(n^3 log n) algorithm computes maximum (weighted) independent sets for disk graphs with all disks on the convex hull, plus O(n^3 log^2 n) for k-dispersion on the same inputs.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.04896","ref_index":19,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Measuring Depth of Matroids","primary_cat":"math.CO","submitted_at":"2026-04-06T17:44:04+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A unified framework yields eight depth measures on matroids with six shown functionally inequivalent, two matching branch-depth and tree-depth, and all coinciding on matroids versus matrices over any field.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}