The content delves into the central path problem in graph theory, focusing on path eccentricity in k-AT-free graphs. It establishes a link between path eccentricity and the consecutive ones property, offering new insights and generalizations. Theorems are proven to show bounds on path eccentricity based on graph properties.
Key points include defining k-AT-free graphs, proving theorems related to path eccentricity bounds, discussing the consecutive ones property, and exploring implications for graph structures. Lemmas are used to demonstrate ordering constraints in induced paths and cycles within graphs with the *-C1P.
The content concludes by showing that graphs with the *-C1P do not contain 2-asteroidal triples, leading to a maximum path eccentricity of 2. This result is illustrated through detailed proofs and references to related works.
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by Paul Bastide... om arxiv.org 03-11-2024
https://arxiv.org/pdf/2403.05360.pdfDiepere vragen