graphs). Kotzig's conjecture was first listed as an open problem by Bondy & Murty in 1976, attributed to Kotzig and dated to 1974. Kotzig's first own...

conjecture or Ringel–Kotzig conjecture, named after Gerhard Ringel and Anton Kotzig, and sometimes abbreviated GTC (not to be confused with Kotzig's conjecture...

Ringel–Kotzig conjecture on graceful labeling of trees (with Gerhard Ringel); Kotzig's conjecture on regularly path connected graphs; Kotzig's theorem...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

with a perfect matching (also called a 1-factor). In 1964, Anton Kotzig conjectured that every complete graph K2n where n ≥ 2 has a perfect 1-factorization...

extensive study. Arguably, the largest unproven conjecture in graph labeling is the Ringel–Kotzig conjecture, which hypothesizes that all trees are graceful...

no such graphs are known, and the claim of their non-existence is Kotzig's conjecture. Central digraph, a directed graph with the property that every two...

2000, six remain unsolved to date: Birch and Swinnerton-Dyer conjecture Hodge conjecture Navier–Stokes existence and smoothness P versus NP Riemann hypothesis...

universal graphs for planar graphs that have n1+o(1) vertices. Sumner's conjecture states that tournaments are universal for polytrees, in the sense that...

It is widely believed that all other instances have a solution. This conjecture is supported by recent non-constructive and asymptotic solutions for large...

graph Wd(k,n) is proved not graceful if k > 5. In 1979, Bermond has conjectured that Wd(4,n) is graceful for all n ≥ 4. Through an equivalence with perfect...

edges are directed from the loser of each game to the winner. Answering a conjecture by Paul Kelly from 1968, Daniela Kühn and Deryk Osthus proved in 2012...

graph with no holes or with a constant number of holes. However, they conjecture that the problem is NP-complete for arbitrary planar graphs, and they...

vertex) has been considered with respect to the Aanderaa–Karp–Rosenberg conjecture on how many queries (subroutine calls) are needed to test whether a labeled...