Further casework can be done to obtain a bound of at most three paths
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
Further casework can be done to obtain a bound of at most three paths. The relationship between treewidth and balanced separators can be further explored. The application of the Grid Theorem of Robertson and Seymour can be further studied.
Evidence profile
Sourced from the stated research gap and future-work section of the source papers, classified as general, drawn from work published between 2024 and 2026, spanning 2 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 3 representative gaps
- Hitting Cycles through Prescribed Vertices or Edges (2026) · SIAM Journal on Discrete Mathematics · doi
The previously known quadratic upper bound for the directed tree-width of a directed graph is not tight. There is a lack of understanding of the corresponding statement in bidirected graphs and its edge-variant in undirected and directed graphs. The vertex-version in undirected graphs remains an open problem.
generalstated research gapKeywords: previously known quadratic upper bound directed tree-width graph - Pathwidth vs Cocircumference (2024) · SIAM Journal on Discrete Mathematics · doi
The paper identifies a gap in the existing literature regarding the relationship between the pathwidth of a graph and its cocircumference. The authors note that no such bound holds for the treedepth of a graph. The paper aims to fill this gap by providing an upper bound on the pathwidth of a 2-connected graph with cocircumference.
generalstated research gapKeywords: paper identifies gap existing literature regarding relationship between - A Simple Layered-Wheel-Like Construction (2026) · The Electronic Journal of Combinatorics · doi
Further casework can be done to obtain a bound of at most three paths. The relationship between treewidth and balanced separators can be further explored. The application of the Grid Theorem of Robertson and Seymour can be further studied.
generalfuture-work sectionevidence 5/5Keywords: further casework done obtain bound three paths relationship
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