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Sub-atomic product of funcoids is a categorical product ★★
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- \item Product morphism is defined similarly to the category of topological spaces. \item Product object is the sub-atomic product. \item Projections are sub-atomic projections.
See details, exact definitions, and attempted proofs here.
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Bounding the on-line choice number in terms of the choice number ★★
Author(s): Zhu

Keywords: choosability; list coloring; on-line choosability
Are almost all graphs determined by their spectrum? ★★★
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Keywords: cospectral; graph invariant; spectrum
Signing a graph to have small magnitude eigenvalues ★★






Keywords: eigenvalue; expander; Ramanujan graph; signed graph; signing
The Bollobás-Eldridge-Catlin Conjecture on graph packing ★★★
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Keywords: graph packing
Decomposing k-arc-strong tournament into k spanning strong digraphs ★★
Author(s): Bang-Jensen; Yeo
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PTAS for feedback arc set in tournaments ★★
Keywords: feedback arc set; PTAS; tournament
Partitionning a tournament into k-strongly connected subtournaments. ★★
Author(s): Thomassen








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Weighted colouring of hexagonal graphs. ★★




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Colouring the square of a planar graph ★★
Author(s): Wegner


- \item at most






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List chromatic number and maximum degree of bipartite graphs ★★
Author(s): Alon




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Hamilton decomposition of prisms over 3-connected cubic planar graphs ★★

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Turán's problem for hypergraphs ★★
Author(s): Turan








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4-connected graphs are not uniquely hamiltonian ★★
Author(s): Fleischner

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Every prism over a 3-connected planar graph is hamiltonian. ★★
Author(s): Kaiser; Král; Rosenfeld; Ryjácek; Voss



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Hoàng-Reed Conjecture ★★★






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Edge-disjoint Hamilton cycles in highly strongly connected tournaments. ★★
Author(s): Thomassen




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Hamilton cycle in small d-diregular graphs ★★
Author(s): Jackson
An directed graph is -diregular if every vertex has indegree and outdegree at least
.



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Switching reconstruction of digraphs ★★
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Switching reconstruction conjecture ★★
Author(s): Stanley
Keywords: reconstruction