This paper deals with the problem of enumerating 3-edge-connected spanning subgraphs of an input plane graph. In 2018, Yamanaka et al. proposed two enumeration algorithms for such a problem. Their algorithm generates each 2-edge-connected spanning subgraph of a given plane graph with n vertices in O(n) time, and another one generates each k-edge-connected spanning subgraph of a general graph with m edges in O(mT) time, where T is the running time to check the k-edge connectivity of a graph. This paper focuses on the case of the 3-edge-connectivity in a plane graph. We give an algorithm which generates each 3-edge-connected spanning subgraph of the input plane graph in O(n2) time. This time complexity is the same as the algorithm by Yamanaka et al., but our algorithm is simpler than theirs.
Yasuko MATSUI
Tokai University
Kenta OZEKI
Yokohama National University
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Yasuko MATSUI, Kenta OZEKI, "A Note on Enumeration of 3-Edge-Connected Spanning Subgraphs in Plane Graphs" in IEICE TRANSACTIONS on Information,
vol. E104-D, no. 3, pp. 389-391, March 2021, doi: 10.1587/transinf.2020FCL0002.
Abstract: This paper deals with the problem of enumerating 3-edge-connected spanning subgraphs of an input plane graph. In 2018, Yamanaka et al. proposed two enumeration algorithms for such a problem. Their algorithm generates each 2-edge-connected spanning subgraph of a given plane graph with n vertices in O(n) time, and another one generates each k-edge-connected spanning subgraph of a general graph with m edges in O(mT) time, where T is the running time to check the k-edge connectivity of a graph. This paper focuses on the case of the 3-edge-connectivity in a plane graph. We give an algorithm which generates each 3-edge-connected spanning subgraph of the input plane graph in O(n2) time. This time complexity is the same as the algorithm by Yamanaka et al., but our algorithm is simpler than theirs.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2020FCL0002/_p
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@ARTICLE{e104-d_3_389,
author={Yasuko MATSUI, Kenta OZEKI, },
journal={IEICE TRANSACTIONS on Information},
title={A Note on Enumeration of 3-Edge-Connected Spanning Subgraphs in Plane Graphs},
year={2021},
volume={E104-D},
number={3},
pages={389-391},
abstract={This paper deals with the problem of enumerating 3-edge-connected spanning subgraphs of an input plane graph. In 2018, Yamanaka et al. proposed two enumeration algorithms for such a problem. Their algorithm generates each 2-edge-connected spanning subgraph of a given plane graph with n vertices in O(n) time, and another one generates each k-edge-connected spanning subgraph of a general graph with m edges in O(mT) time, where T is the running time to check the k-edge connectivity of a graph. This paper focuses on the case of the 3-edge-connectivity in a plane graph. We give an algorithm which generates each 3-edge-connected spanning subgraph of the input plane graph in O(n2) time. This time complexity is the same as the algorithm by Yamanaka et al., but our algorithm is simpler than theirs.},
keywords={},
doi={10.1587/transinf.2020FCL0002},
ISSN={1745-1361},
month={March},}
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TY - JOUR
TI - A Note on Enumeration of 3-Edge-Connected Spanning Subgraphs in Plane Graphs
T2 - IEICE TRANSACTIONS on Information
SP - 389
EP - 391
AU - Yasuko MATSUI
AU - Kenta OZEKI
PY - 2021
DO - 10.1587/transinf.2020FCL0002
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E104-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2021
AB - This paper deals with the problem of enumerating 3-edge-connected spanning subgraphs of an input plane graph. In 2018, Yamanaka et al. proposed two enumeration algorithms for such a problem. Their algorithm generates each 2-edge-connected spanning subgraph of a given plane graph with n vertices in O(n) time, and another one generates each k-edge-connected spanning subgraph of a general graph with m edges in O(mT) time, where T is the running time to check the k-edge connectivity of a graph. This paper focuses on the case of the 3-edge-connectivity in a plane graph. We give an algorithm which generates each 3-edge-connected spanning subgraph of the input plane graph in O(n2) time. This time complexity is the same as the algorithm by Yamanaka et al., but our algorithm is simpler than theirs.
ER -