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October 2, 2025Open Access

Solution to a problem on isolation of 3-vertex paths

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Authors

KBKarl BartoloPBPeter BorgDSDayle Scicluna

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Overview

Determining the 3-path isolation number in graphs without induced cycles, suggesting a limit of n/4.

Key Points

  • The 3-path isolation number of connected graphs with no induced 6-cycles is bounded by n/4.
  • For graphs lacking induced 6-cycles, the maximum isolation number remains less than or equal to n/4.
  • A new method was introduced showing the decrease in the isolation number upon removing vertices.
  • The findings indicate potential applications for analyzing graph structures beyond the current scope.

Cite This Study

Bartolo et al. (2025) studied this question.

synapsesocial.com/papers/68de84bf5b556a9128e1bd07https://doi.org/10.48550/arxiv.2506.19149
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