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Exact Tie-Breaking and Tight Degree Bounds for Minimum-Degree Greedy on Interval Graphs — arXiv:2611.01796

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01796
License (as archived): CC0-1.0
Archived: 2026-11-03T11:45:40.755Z
SHA-256 of the archived text: 8d5561ec9d16dd47e4c9aecbbe698f910c694eca6d683723325cdf732ff45556
Stable URL of this page: https://metraipolis.com/documento/dc_7d95efd9ef99

How to cite

Exact Tie-Breaking and Tight Degree Bounds for Minimum-Degree Greedy on Interval Graphs — arXiv:2611.01796 — arXiv (en), https://arxiv.org/abs/2611.01796 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7d95efd9ef99 (Metraipolis archive dc_7d95efd9ef99, sha256 8d5561ec9d16dd47e4c9aecbbe698f910c694eca6d683723325cdf732ff45556)

BibTeX

@misc{dc7d95efd9ef99,
  title = {Exact Tie-Breaking and Tight Degree Bounds for Minimum-Degree Greedy on Interval Graphs — arXiv:2611.01796},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01796},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7d95efd9ef99; sha256 8d5561ec9d16dd47e4c9aecbbe698f910c694eca6d683723325cdf732ff45556},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01796. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Minimum-degree greedy repeatedly selects a vertex of minimum current degree and deletes its closed neighborhood; let $B(G)$ and $W(G)$ be its largest and smallest output sizes over complete legal executions. Given a closed interval representation of an $n$-vertex graph, we compute both values and construct attaining executions in $O(n^3)$ time and $O(n^2)$ space using endpoint-window dynamic programming and legal interleaving. For interval graphs with $\Delta(G)\le4$, we prove the tight bound $B(G)\ge3\alpha(G)/4$ by reduction to unit interval graphs and induction with virtual boundary vertices. A connected unit interval family $J_t$ attains equality, with $B(J_t)=W(J_t)=3t$ and $\alpha(J_t)=4t$. For each degree bound $d\ge5$, a degree-five family $H_t$ approaches the known $2/3$ lower bound, giving infimum $2/3$. Together with known optimal favorable tie-breaking for $d\le3$, these results determine the favorable guarantee for every degree bound.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv cs.DS, nuovi lavori del giorno).
Categorie arXiv: Data Structures and Algorithms (cs.DS).
Pagina del lavoro: https://arxiv.org/abs/2611.01796 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T11:07:52.240Z dalla pagina https://arxiv.org/list/cs.DS/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).