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Graph Theory
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¿Are critical k-forests tight?
Strausz
✭✭
0
Hypergraphs
Dino
Woodall's Conjecture
Woodall
✭✭✭
0
Directed Graphs
mdevos
What is the smallest number of disjoint spanning trees made a graph Hamiltonian
Goldengorin
✭✭
0
Extremal G.T.
boris
What is the largest graph of positive curvature?
DeVos
;
Mohar
✭
1
Topological G.T.
»
Planar graphs
mdevos
Weighted colouring of hexagonal graphs.
McDiarmid
;
Reed
✭✭
0
Coloring
»
Vertex coloring
fhavet
Weak saturation of the cube in the clique
Morrison
;
Noel
✭
1
Extremal G.T.
Jon Noel
Weak pentagon problem
Samal
✭✭
0
Coloring
»
Homomorphisms
Robert Samal
Vertex Coloring of graph fractional powers
Iradmusa
✭✭✭
1
Iradmusa
Universal Steiner triple systems
Grannell
;
Griggs
;
Knor
;
Skoviera
✭✭
0
Coloring
»
Edge coloring
macajova
Universal point sets for planar graphs
Mohar
✭✭✭
0
Topological G.T.
»
Drawings
mdevos
Universal highly arc transitive digraphs
Cameron
;
Praeger
;
Wormald
✭✭✭
0
Infinite Graphs
mdevos
Unit vector flows
Jain
✭✭
0
Coloring
»
Nowhere-zero flows
mdevos
Unions of triangle free graphs
Erdos
;
Hajnal
✭✭✭
0
Infinite Graphs
mdevos
Unfriendly partitions
Cowan
;
Emerson
✭✭✭
0
Infinite Graphs
mdevos
Turán's problem for hypergraphs
Turan
✭✭
0
Hypergraphs
fhavet
Turán number of a finite family.
Erdos
;
Simonovits
✭✭
0
fhavet
Triangle-packing vs triangle edge-transversal.
Tuza
✭✭
0
Extremal G.T.
fhavet
Triangle free strongly regular graphs
✭✭✭
0
Algebraic G.T.
mdevos
Total Colouring Conjecture
Behzad
✭✭✭
0
Coloring
Iradmusa
Three-chromatic (0,2)-graphs
Payan
✭✭
0
Coloring
Gordon Royle
The Two Color Conjecture
Neumann-Lara
✭✭
0
Directed Graphs
mdevos
The three 4-flows conjecture
DeVos
✭✭
0
Coloring
»
Nowhere-zero flows
mdevos
The stubborn list partition problem
Cameron
;
Eschen
;
Hoang
;
Sritharan
✭✭
0
Graph Algorithms
mdevos
The intersection of two perfect matchings
Macajova
;
Skoviera
✭✭
0
Basic G.T.
»
Matchings
mdevos
The Erdös-Hajnal Conjecture
Erdos
;
Hajnal
✭✭✭
0
Extremal G.T.
mdevos
The Crossing Number of the Hypercube
Erdos
;
Guy
✭✭
0
Topological G.T.
»
Crossing numbers
Robert Samal
The Crossing Number of the Complete Graph
✭✭✭
0
Topological G.T.
»
Crossing numbers
Robert Samal
The Crossing Number of the Complete Bipartite Graph
Turan
✭✭✭
0
Topological G.T.
»
Crossing numbers
Robert Samal
The circular embedding conjecture
Haggard
✭✭✭
0
Basic G.T.
»
Cycles
mdevos
The Borodin-Kostochka Conjecture
Borodin
;
Kostochka
✭✭
0
Andrew King
The Bollobás-Eldridge-Catlin Conjecture on graph packing
✭✭✭
0
Extremal G.T.
asp
The Bermond-Thomassen Conjecture
Bermond
;
Thomassen
✭✭
0
Directed Graphs
JS
The Berge-Fulkerson conjecture
Berge
;
Fulkerson
✭✭✭✭
0
Basic G.T.
»
Matchings
mdevos
Switching reconstruction of digraphs
Bondy
;
Mercier
✭✭
0
fhavet
Switching reconstruction conjecture
Stanley
✭✭
0
fhavet
Subgraph of large average degree and large girth.
Thomassen
✭✭
0
Basic G.T.
fhavet
Subdivision of a transitive tournament in digraphs with large outdegree.
Mader
✭✭
0
Directed Graphs
fhavet
Strong matchings and covers
Aharoni
✭✭✭
0
Infinite Graphs
mdevos
Strong edge colouring conjecture
Erdos
;
Nesetril
✭✭
0
Coloring
»
Edge coloring
fhavet
Strong colorability
Aharoni
;
Alon
;
Haxell
✭✭✭
0
Coloring
»
Vertex coloring
berger
Strong 5-cycle double cover conjecture
Arthur
;
Hoffmann-Ostenhof
✭✭✭
1
Basic G.T.
»
Cycles
arthur
Star chromatic index of cubic graphs
Dvorak
;
Mohar
;
Samal
✭✭
0
Robert Samal
Star chromatic index of complete graphs
Dvorak
;
Mohar
;
Samal
✭✭
1
Robert Samal
Stable set meeting all longest directed paths.
Laborde
;
Payan
;
Xuong N.H.
✭✭
0
fhavet
Splitting a digraph with minimum outdegree constraints
Alon
✭✭✭
0
Directed Graphs
fhavet
Simultaneous partition of hypergraphs
Kühn
;
Osthus
✭✭
0
Hypergraphs
fhavet
Signing a graph to have small magnitude eigenvalues
Bilu
;
Linial
✭✭
0
mdevos
Sidorenko's Conjecture
Sidorenko
✭✭✭
0
Jon Noel
Shuffle-Exchange Conjecture (graph-theoretic form)
Beneš
;
Folklore
;
Stone
✭✭✭
0
Vadim Lioubimov
Shannon capacity of the seven-cycle
✭✭✭
0
tchow
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