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Černý's conjecture

No description available.

Erdős–Gyárfás conjecture

In graph theory, the unproven Erdős–Gyárfás conjecture, made in 1995 by the prolific mathematician Paul Erdős and his collaborator András Gyárfás, states that every graph with minimum degree 3 contain

Lovász conjecture

In graph theory, the Lovász conjecture (1969) is a classical problem on Hamiltonian paths in graphs. It says: Every finite connected vertex-transitive graph contains a Hamiltonian path. Originally Lás

Gilbert–Pollack conjecture

No description available.

Szymanski's conjecture

In mathematics, Szymanski's conjecture, named after Ted H. Szymanski, states that every permutation on the n-dimensional doubly directed hypercube graph can be routed with edge-disjoint paths. That is

Oberwolfach problem

The Oberwolfach problem is an unsolved problem in mathematics that may be formulated either as a problem of scheduling seating assignments for diners,or more abstractly as a problem in graph theory, o

Erdős–Faber–Lovász conjecture

In graph theory, the Erdős–Faber–Lovász conjecture is a problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972. It says: If k complete graphs,

Turán's brick factory problem

Unsolved problem in mathematics: Can any complete bipartite graph be drawn with fewer crossings than the number given by Zarankiewicz? (more unsolved problems in mathematics) In the mathematics of gra

Vizing's conjecture

In graph theory, Vizing's conjecture concerns a relation between the domination number and the cartesian product of graphs. This conjecture was first stated by Vadim G. Vizing, and states that, if γ(G

Barnette's conjecture

Barnette's conjecture is an unsolved problem in graph theory, a branch of mathematics, concerning Hamiltonian cycles in graphs. It is named after , a professor emeritus at the University of California

Zarankiewicz problem

The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgr

Cycle double cover

In graph-theoretic mathematics, a cycle double cover is a collection of cycles in an undirected graph that together include each edge of the graph exactly twice. For instance, for any polyhedral graph

Unfriendly partition

In the mathematics of infinite graphs, an unfriendly partition or majority coloring is a partition of the vertices of the graph into disjoint subsets, so that every vertex has at least as many neighbo

Sumner's conjecture

Sumner's conjecture (also called Sumner's universal tournament conjecture) states that every orientation of every -vertex tree is a subgraph of every -vertex tournament. David Sumner, a graph theorist

Hadwiger–Nelson problem

In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson, asks for the minimum number of colors required to color the plane such that no two points at distan

Albertson conjecture

In combinatorial mathematics, the Albertson conjecture is an unproven relationship between the crossing number and the chromatic number of a graph. It is named after Michael O. Albertson, a professor

Erdős on Graphs

Erdős on Graphs: His Legacy of Unsolved Problems is a book on unsolved problems in mathematics collected by Paul Erdős in the area of graph theory. It was written by Fan Chung and Ronald Graham, based

Conway's 99-graph problem

In graph theory, Conway's 99-graph problem is an unsolved problem asking whether there exists an undirected graph with 99 vertices, in which each two adjacent vertices have exactly one common neighbor

Gyárfás–Sumner conjecture

In graph theory, the Gyárfás–Sumner conjecture asks whether, for every tree and complete graph , the graphs with neither nor as induced subgraphs can be properly colored using only a constant number o

Černý conjecture

No description available.

Hadwiger conjecture (graph theory)

In graph theory, the Hadwiger conjecture states that if is loopless and has no minor then its chromatic number satisfies . It is known to be true for . The conjecture is a generalization of the four-c

GNRS conjecture

In theoretical computer science and metric geometry, the GNRS conjecture connects the theory of graph minors, the stretch factor of embeddings, and the approximation ratio of multi-commodity flow prob

Reconstruction conjecture

Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to Kelly and Ulam.

Babai's problem

In algebraic graph theory, Babai's problem was proposed in 1979 by László Babai.

Brouwer's conjecture

In the mathematical field of spectral graph theory, Brouwer's conjecture is a conjecture by Andries Brouwer on upper bounds for the intermediate sums of the eigenvalues of the Laplacian of a graph in

Erdős–Hajnal conjecture

In graph theory, a branch of mathematics, the Erdős–Hajnal conjecture states that families of graphs defined by forbidden induced subgraphs have either large cliques or large independent sets. It is n

New digraph reconstruction conjecture

The reconstruction conjecture of Stanisław Ulam is one of the best-known open problems in graph theory. Using the terminology of Frank Harary it can be stated as follows: If G and H are two graphs on

Harborth's conjecture

In mathematics, Harborth's conjecture states that every planar graph has a planar drawing in which every edge is a straight segment of integer length. This conjecture is named after Heiko Harborth, an

Second neighborhood problem

In mathematics, the second neighborhood problem is an unsolved problem about oriented graphs posed by Paul Seymour. Intuitively, it suggests that in a social network described by such a graph, someone

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