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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Open problems around exact algorithms by Gerhard J. Woeginger, Discrete Applied Mathematics 156 (2008) 397–405. The RTA list of open problems – open problems in rewriting. The TLCA List of Open Problems – open problems in area typed lambda calculus
This book is a classic, developing the theory, then cataloguing many NP-Complete problems. Cook, S.A. (1971). "The complexity of theorem proving procedures". Proceedings, Third Annual ACM Symposium on the Theory of Computing, ACM, New York. pp. 151– 158. doi: 10.1145/800157.805047. Karp, Richard M. (1972). "Reducibility among combinatorial ...
The reconstruction conjecture of Stanisław Ulam is one of the best-known open problems in graph theory.Using the terminology of Frank Harary [1] it can be stated as follows: If G and H are two graphs on at least three vertices and ƒ is a bijection from V(G) to V(H) such that G\{v} and H\{ƒ(v)} are isomorphic for all vertices v in V(G), then G and H are isomorphic.
The possibility of a graph with these parameters was already suggested in 1969 by Norman L. Biggs, [6] and its existence noted as an open problem by others before Conway. [3] [7] [8] [9] Conway himself had worked on the problem as early as 1975, [7] but offered the prize in 2014 as part of a set of problems posed in the DIMACS Conference on Challenges of Identifying Integer Sequences.
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 named for Paul Erdős and András Hajnal, who first posed it as an open problem in a paper from 1977. [1]
A hypothetical graph (or more than one) of diameter 2, girth 5, degree 57 and order 3250; the existence of such is unknown and is one of the most famous open problems in graph theory. [ 4 ] Although all the known Moore graphs are vertex-transitive graphs , the unknown one (if it exists) cannot be vertex-transitive, as its automorphism group can ...