A (2, 1)-Decomposition of Planar Graphs Without Intersecting 3-Cycles and Adjacent 4--Cycles
Let G be a graph. For two positive integers d and h , a ( d , h )- decomposition of G is a pair ( G , H ) such that H is a subgraph of G of maximum degree at most h and D is an acyclic orientation of G - E ( H ) of maximum out-degree at most d . A graph G is ( d , h )- decomposable if G has a ( d...
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| Veröffentlicht in: | Graphs and combinatorics 2023-12, Vol.39 (6), Article 115 |
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| creator | Tian, Fangyu Li, Xiangwen |
| description | Let
G
be a graph. For two positive integers
d
and
h
, a (
d
,
h
)-
decomposition
of
G
is a pair (
G
,
H
) such that
H
is a subgraph of
G
of maximum degree at most
h
and
D
is an acyclic orientation of
G
-
E
(
H
)
of maximum out-degree at most
d
. A graph
G
is (
d
,
h
)-
decomposable
if
G
has a (
d
,
h
)-decomposition. In this paper, we prove that every planar graph without intersecting 3-cycles and adjacent
4
-
-cycles is (2, 1)-decomposable. As a corollary, we obtain that every planar graph without intersecting 3-cycles and adjacent
4
-
-cycles has a matching
M
such that
G
-
M
is 2-degenerate and hence
G
-
M
is DP-3-colorable and Alon-Tarsi number of
G
-
M
is at most 3. |
| doi_str_mv | 10.1007/s00373-023-02708-x |
| format | Article |
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G
be a graph. For two positive integers
d
and
h
, a (
d
,
h
)-
decomposition
of
G
is a pair (
G
,
H
) such that
H
is a subgraph of
G
of maximum degree at most
h
and
D
is an acyclic orientation of
G
-
E
(
H
)
of maximum out-degree at most
d
. A graph
G
is (
d
,
h
)-
decomposable
if
G
has a (
d
,
h
)-decomposition. In this paper, we prove that every planar graph without intersecting 3-cycles and adjacent
4
-
-cycles is (2, 1)-decomposable. As a corollary, we obtain that every planar graph without intersecting 3-cycles and adjacent
4
-
-cycles has a matching
M
such that
G
-
M
is 2-degenerate and hence
G
-
M
is DP-3-colorable and Alon-Tarsi number of
G
-
M
is at most 3.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-023-02708-x</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Combinatorics ; Decomposition ; Engineering Design ; Graph theory ; Mathematics ; Mathematics and Statistics ; Original Paper</subject><ispartof>Graphs and combinatorics, 2023-12, Vol.39 (6), Article 115</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-596e6dc6e33d0fb0f32c9b7f65d3c930b7fcf5f3ae373cdabcd26a387f150a7b3</cites><orcidid>0000-0001-9328-0766</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00373-023-02708-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-023-02708-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Tian, Fangyu</creatorcontrib><creatorcontrib>Li, Xiangwen</creatorcontrib><title>A (2, 1)-Decomposition of Planar Graphs Without Intersecting 3-Cycles and Adjacent 4--Cycles</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>Let
G
be a graph. For two positive integers
d
and
h
, a (
d
,
h
)-
decomposition
of
G
is a pair (
G
,
H
) such that
H
is a subgraph of
G
of maximum degree at most
h
and
D
is an acyclic orientation of
G
-
E
(
H
)
of maximum out-degree at most
d
. A graph
G
is (
d
,
h
)-
decomposable
if
G
has a (
d
,
h
)-decomposition. In this paper, we prove that every planar graph without intersecting 3-cycles and adjacent
4
-
-cycles is (2, 1)-decomposable. As a corollary, we obtain that every planar graph without intersecting 3-cycles and adjacent
4
-
-cycles has a matching
M
such that
G
-
M
is 2-degenerate and hence
G
-
M
is DP-3-colorable and Alon-Tarsi number of
G
-
M
is at most 3.</description><subject>Combinatorics</subject><subject>Decomposition</subject><subject>Engineering Design</subject><subject>Graph theory</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><issn>0911-0119</issn><issn>1435-5914</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LAzEQDaJgrf4BTwEvCkYnm_08lqq1IOhB8SQhm03aLW2yJim0_8bf4i8zdQvePAwzDO-9efMQOqdwQwGKWw_ACkYg2VUBJdkcoAFNWUayiqaHaAAVpQQorY7RifcLAMhoCgP0McKXyfX3F70id0raVWd9G1prsNX4ZSmMcHjiRDf3-L0Nc7sOeGqCcl7J0JoZZmS8lUvlsTANHjULIZUJOCX79Sk60mLp1dm-D9Hbw_3r-JE8PU-m49ETkdFsiB5zlTcyV4w1oGvQLJFVXeg8a5isGMRR6kwzoeKTshG1bJJcsLLQNANR1GyILnrdztnPtfKBL-zamXiSJ2XBipJVWRVRSY-SznrvlOada1fCbTkFvouR9zHyGCP_jZFvIon1JB_BZqbcn_Q_rB_biXWc</recordid><startdate>20231201</startdate><enddate>20231201</enddate><creator>Tian, Fangyu</creator><creator>Li, Xiangwen</creator><general>Springer Japan</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-9328-0766</orcidid></search><sort><creationdate>20231201</creationdate><title>A (2, 1)-Decomposition of Planar Graphs Without Intersecting 3-Cycles and Adjacent 4--Cycles</title><author>Tian, Fangyu ; Li, Xiangwen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-596e6dc6e33d0fb0f32c9b7f65d3c930b7fcf5f3ae373cdabcd26a387f150a7b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Combinatorics</topic><topic>Decomposition</topic><topic>Engineering Design</topic><topic>Graph theory</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tian, Fangyu</creatorcontrib><creatorcontrib>Li, Xiangwen</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Graphs and combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tian, Fangyu</au><au>Li, Xiangwen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A (2, 1)-Decomposition of Planar Graphs Without Intersecting 3-Cycles and Adjacent 4--Cycles</atitle><jtitle>Graphs and combinatorics</jtitle><stitle>Graphs and Combinatorics</stitle><date>2023-12-01</date><risdate>2023</risdate><volume>39</volume><issue>6</issue><artnum>115</artnum><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>Let
G
be a graph. For two positive integers
d
and
h
, a (
d
,
h
)-
decomposition
of
G
is a pair (
G
,
H
) such that
H
is a subgraph of
G
of maximum degree at most
h
and
D
is an acyclic orientation of
G
-
E
(
H
)
of maximum out-degree at most
d
. A graph
G
is (
d
,
h
)-
decomposable
if
G
has a (
d
,
h
)-decomposition. In this paper, we prove that every planar graph without intersecting 3-cycles and adjacent
4
-
-cycles is (2, 1)-decomposable. As a corollary, we obtain that every planar graph without intersecting 3-cycles and adjacent
4
-
-cycles has a matching
M
such that
G
-
M
is 2-degenerate and hence
G
-
M
is DP-3-colorable and Alon-Tarsi number of
G
-
M
is at most 3.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s00373-023-02708-x</doi><orcidid>https://orcid.org/0000-0001-9328-0766</orcidid></addata></record> |
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| ispartof | Graphs and combinatorics, 2023-12, Vol.39 (6), Article 115 |
| issn | 0911-0119 1435-5914 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Combinatorics Decomposition Engineering Design Graph theory Mathematics Mathematics and Statistics Original Paper |
| title | A (2, 1)-Decomposition of Planar Graphs Without Intersecting 3-Cycles and Adjacent 4--Cycles |
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