Selected Neighbor Degree Forest Realization

Amotz Bar-Noy; David Peleg; Dror Rawitz; Elad Yehezkel

doi:10.4230/LIPIcs.ISAAC.2021.27

Selected Neighbor Degree Forest Realization

Amotz Bar-Noy, David Peleg, Dror Rawitz, Elad Yehezkel

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The classical degree realization problem is defined as follows: Given a sequence d^¯ = (d1, . . ., dn) of positive integers, construct an n-vertex graph in which each vertex ui has degree di (or decide that no such graph exists). In this article, we present and study the related selected neighbor degree realization problem, which requires that each vertex ui of G has a neighbor of degree di. We solve the problem when G is required to be acyclic (i.e., a forest), and present a sufficient and necessary condition for a given sequence to be realizable.

Original language	English
Title of host publication	32nd International Symposium on Algorithms and Computation, ISAAC 2021
Editors	Hee-Kap Ahn, Kunihiko Sadakane
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959772143
DOIs	https://doi.org/10.4230/LIPIcs.ISAAC.2021.27
State	Published - 1 Dec 2021
Event	32nd International Symposium on Algorithms and Computation, ISAAC 2021 - Fukuoka, Japan Duration: 6 Dec 2021 → 8 Dec 2021

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	212
ISSN (Print)	1868-8969

Conference

Conference	32nd International Symposium on Algorithms and Computation, ISAAC 2021
Country/Territory	Japan
City	Fukuoka
Period	6/12/21 → 8/12/21

Bibliographical note

Publisher Copyright:
© Amotz Bar-Noy, David Peleg, Dror Rawitz, and Elad Yehezkel.

Funding

Supported in part by a US-Israel BSF grant (2018043).

Funders	Funder number
US-Israel BSF	2018043

Keywords

Graph algorithms
Lower bound
Network realization

Access to Document

10.4230/LIPIcs.ISAAC.2021.27

Cite this

Bar-Noy, A., Peleg, D., Rawitz, D., & Yehezkel, E. (2021). Selected Neighbor Degree Forest Realization. In H.-K. Ahn, & K. Sadakane (Eds.), 32nd International Symposium on Algorithms and Computation, ISAAC 2021 Article 27 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 212). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2021.27

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abstract = "The classical degree realization problem is defined as follows: Given a sequence d¯ = (d1, . . ., dn) of positive integers, construct an n-vertex graph in which each vertex ui has degree di (or decide that no such graph exists). In this article, we present and study the related selected neighbor degree realization problem, which requires that each vertex ui of G has a neighbor of degree di. We solve the problem when G is required to be acyclic (i.e., a forest), and present a sufficient and necessary condition for a given sequence to be realizable.",

keywords = "Graph algorithms, Lower bound, Network realization",

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Bar-Noy, A, Peleg, D, Rawitz, D & Yehezkel, E 2021, Selected Neighbor Degree Forest Realization. in H-K Ahn & K Sadakane (eds), 32nd International Symposium on Algorithms and Computation, ISAAC 2021., 27, Leibniz International Proceedings in Informatics, LIPIcs, vol. 212, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 32nd International Symposium on Algorithms and Computation, ISAAC 2021, Fukuoka, Japan, 6/12/21. https://doi.org/10.4230/LIPIcs.ISAAC.2021.27

Selected Neighbor Degree Forest Realization. / Bar-Noy, Amotz; Peleg, David; Rawitz, Dror et al.
32nd International Symposium on Algorithms and Computation, ISAAC 2021. ed. / Hee-Kap Ahn; Kunihiko Sadakane. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2021. 27 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 212).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Bar-Noy A, Peleg D, Rawitz D, Yehezkel E. Selected Neighbor Degree Forest Realization. In Ahn HK, Sadakane K, editors, 32nd International Symposium on Algorithms and Computation, ISAAC 2021. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2021. 27. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.ISAAC.2021.27

Selected Neighbor Degree Forest Realization

Abstract

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Bibliographical note

Funding

Keywords

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