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Open Problems


TitleAuthor(s)Imp.¹Rec.²sort iconArea » Topic » SubtopicPosted by
Switching reconstruction conjectureStanley✭✭0Graph Theoryfhavet
Switching reconstruction of digraphsBondy; Mercier✭✭0Graph Theoryfhavet
Hamilton cycle in small d-diregular graphsJackson✭✭0Graph Theory » Directed Graphsfhavet
Edge-disjoint Hamilton cycles in highly strongly connected tournaments.Thomassen✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
Hoàng-Reed ConjectureHoang; Reed✭✭✭0Graph Theory » Directed Graphsfhavet
Every prism over a 3-connected planar graph is hamiltonian.Kaiser; Král; Rosenfeld; Ryjácek; Voss✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
4-connected graphs are not uniquely hamiltonianFleischner✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
Turán's problem for hypergraphsTuran✭✭0Graph Theory » Hypergraphsfhavet
Hamilton decomposition of prisms over 3-connected cubic planar graphsAlspach; Rosenfeld✭✭0Graph Theory » Basic G.T. » Cyclesfhavet
List chromatic number and maximum degree of bipartite graphsAlon✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Colouring the square of a planar graphWegner✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Weighted colouring of hexagonal graphs.McDiarmid; Reed✭✭0Graph Theory » Coloring » Vertex coloringfhavet
Partitionning a tournament into k-strongly connected subtournaments.Thomassen✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
PTAS for feedback arc set in tournamentsAilon; Alon✭✭0Graph Theory » Graph Algorithmsfhavet
Decomposing k-arc-strong tournament into k spanning strong digraphsBang-Jensen; Yeo✭✭0Graph Theory » Directed Graphs » Tournamentsfhavet
The Bollobás-Eldridge-Catlin Conjecture on graph packing✭✭✭0Graph Theory » Extremal G.T.asp
Signing a graph to have small magnitude eigenvaluesBilu; Linial✭✭0Graph Theorymdevos
Are almost all graphs determined by their spectrum?✭✭✭0Graph Theorymdevos
Sub-atomic product of funcoids is a categorical product✭✭0Algebraporton
Closing Lemma for Diffeomorphism (Dynamical Systems)Charles Pugh✭✭✭✭0TopologyJailton Viana
Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)✭✭✭✭0TopologyJailton Viana
Arc-disjoint directed cycles in regular directed graphsAlon; McDiarmid; Molloy✭✭0Graph Theory » Directed Graphsfhavet
Minimum number of arc-disjoint transitive subtournaments of order 3 in a tournamentYuster✭✭0Graph Theoryfhavet
inverse of an integer matrixGregory✭✭0Algebralvoyster
Cyclic spanning subdigraph with small cyclomatic numberBondy✭✭0Graph Theory » Directed Graphsfhavet
P vs. BPPFolklore✭✭✭0Theoretical Comp. Sci. » Complexity » DerandomizationCharles R Great...
Large acyclic induced subdigraph in a planar oriented graph.Harutyunyan✭✭0Graph Theory » Directed Graphsfhavet
Erdős-Posa property for long directed cyclesHavet; Maia✭✭0Graph Theory » Directed Graphsfhavet
Are all Fermat Numbers square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there only finite Fermat Primes?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Erdős–Faber–Lovász conjectureErdos; Faber; Lovasz✭✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
2-colouring a graph without a monochromatic maximum cliqueHoang; McDiarmid✭✭0Graph Theory » Coloring » Vertex coloringJon Noel
Kriesell's ConjectureKriesell✭✭0Graph Theory » Basic G.T. » ConnectivityJon Noel
List Total Colouring ConjectureBorodin; Kostochka; Woodall✭✭0Graph Theory » ColoringJon Noel
Decomposition of completions of reloidsPorton✭✭0Topologyporton
Every metamonovalued funcoid is monovaluedPorton✭✭0Topologyporton
Every metamonovalued reloid is monovaluedPorton✭✭0Topologyporton
Imbalance conjectureKozerenko✭✭0Graph TheorySergiy Kozerenko
Graphs of exact colorings✭✭0Algebrasabisood
Roller Coaster permutationsAhmed; Snevily✭✭✭0CombinatoricsTanbir Ahmed
Dirac's ConjectureDirac✭✭0GeometryDavid Wood
Generalized path-connectedness in proximity spacesPorton✭✭0Topologyporton
Direct proof of a theorem about compact funcoidsPorton✭✭0Topologyporton
General position subsetsGowers✭✭0GeometryDavid Wood
List Hadwiger ConjectureKawarabayashi; Mohar✭✭0Graph Theory » Coloring » Vertex coloringDavid Wood
Chromatic Number of Common GraphsHatami; Hladký; Kráľ; Norine; Razborov✭✭0Graph TheoryDavid Wood
One-way functions exist✭✭✭✭0Theoretical Comp. Sci. » Complexityporton
Another conjecture about reloids and funcoidsPorton✭✭0Topologyporton
What are hyperfuncoids isomorphic to?Porton✭✭0Topologyporton
Are all Mersenne Numbers with prime exponent square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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