How many papers support this gap analysis?

3 papers from our local library contribute to this synthesis, with an average publication year of 2005.

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mathematics3 papersavg year 2005weak evidence

The existence of Hamilton cycles in connected

Research gap analysis derived from 3 mathematics papers in our local library.

The gap

The existence of Hamilton cycles in connected vertex-transitive graphs is a core open problem in algebraic graph theory, originating from Lovász's 1969 conjecture.

Evidence profile

Sourced from the stated research gap and abstract of the source papers, classified as general, drawn from work published between 1964 and 2026, spanning 3 journals.

Research trend

Established — well-defined area with open sub-problems.

Supporting evidence — 3 representative gaps

Retractions Onto Spheres (1964) · American Mathematical Monthly · doi
The lack of a systematic approach to constructing Hamiltonian cycles and factors. The lack of a necessary and sufficient condition for a graph to possess a factor.
generalstated research gap
Keywords: lack systematic approach constructing hamiltonian cycles factors necessary
Transversal Hamilton Paths and Cycles (2026) · SIAM Journal on Discrete Mathematics · doi
The paper identifies a gap in current research, which is the lack of characterization of graph collections with certain properties. The paper fills this gap by establishing a minimum degree condition and characterizing graph collections with minimum degree at least n-1 2 and without transversal Hamilton cycles.
generalstated research gapevidence 5/5
Keywords: paper identifies gap current research lack characterization graph
On Hamilton cycles in connected vertex-transitive graphs of order $2pq$ (2026) · arXiv
The existence of Hamilton cycles in connected vertex-transitive graphs is a core open problem in algebraic graph theory, originating from Lovász's 1969 conjecture.
generalabstractevidence 5/5
Keywords: existence hamilton cycles connected vertex transitive graphs core open problem algebraic graph theory originating conjecture

Questions about this gap

The existence of Hamilton cycles in connected vertex-transitive graphs is a core open problem in algebraic graph theory, originating from Lovász's 1969 conjecture. This is supported by 3 representative gap statements extracted from 3 papers, rated weak evidence.

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