How many papers support this gap analysis?

3 papers from our local library contribute to this synthesis, with an average publication year of 2013.

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mathematics3 papersavg year 2013weak evidence

To further improve the constant in the Crossing Lemma

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

The gap

To further improve the constant in the Crossing Lemma. To apply the new technique to other graph classes. To explore the applications of the paper's results.

Evidence profile

Sourced from the future-work section and stated research gap of the source papers, classified as general, drawn from work published between 1973 and 2026, spanning 3 journals.

Research trend

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

Supporting evidence — 4 representative gaps

Crossing Number Problems (1973) · American Mathematical Monthly · doi
The paper suggests investigating the rectilinear crossing number of other graphs. The authors propose exploring the relationship between rectilinear crossing numbers and convex k-gons.
generalfuture-work section
Keywords: paper suggests investigating rectilinear crossing number other graphs
On Minimal k‐Factor‐Critical Planar Graphs (2026) · Journal of Graph Theory · doi
The lack of a proof for planar graphs is a gap in the literature. The conjecture was posed by Favaron and Shi in 1998 but remained unproven for planar graphs.
generalstated research gapevidence 5/5
Keywords: lack proof planar graphs gap literature conjecture was
Improving the Crossing Lemma by Characterizing Dense 2-Planar and 3-Planar Graphs (2026) · Journal of Graph Algorithms and Applications · doi
The paper identifies a gap in the current bounds for the crossing number of a given graph. The paper identifies a need for a new technique to characterize dense 2-planar and 3-planar graphs.
generalstated research gapevidence 5/5
Keywords: paper identifies gap current bounds crossing number given
Improving the Crossing Lemma by Characterizing Dense 2-Planar and 3-Planar Graphs (2026) · Journal of Graph Algorithms and Applications · doi
To further improve the constant in the Crossing Lemma. To apply the new technique to other graph classes. To explore the applications of the paper's results.
generalfuture-work sectionevidence 5/5
Keywords: further improve constant crossing lemma apply new technique

Questions about this gap

To further improve the constant in the Crossing Lemma. To apply the new technique to other graph classes. To explore the applications of the paper's results. This is supported by 4 representative gap statements extracted from 3 papers, rated weak evidence.

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