A Tight Linear Bound to the Chromatic Number of (P5,K1+(K1∪K3))-Free Graphs
Let F 1 and F 2 be two disjoint graphs. The union F 1 ∪ F 2 is a graph with vertex set V ( F 1 ) ∪ V ( F 2 ) and edge set E ( F 1 ) ∪ E ( F 2 ) , and the join F 1 + F 2 is a graph with vertex set V ( F 1 ) ∪ V ( F 2 ) and edge set E ( F 1 ) ∪ E ( F 2 ) ∪ { x y | x ∈ V ( F 1 ) and y ∈ V ( F 2 ) } . I...
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| Veröffentlicht in: | Graphs and combinatorics 2023-06, Vol.39 (3), Article 43 |
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| creator | Dong, Wei Xu, Baogang Xu, Yian |
| description | Let
F
1
and
F
2
be two disjoint graphs. The union
F
1
∪
F
2
is a graph with vertex set
V
(
F
1
)
∪
V
(
F
2
)
and edge set
E
(
F
1
)
∪
E
(
F
2
)
, and the join
F
1
+
F
2
is a graph with vertex set
V
(
F
1
)
∪
V
(
F
2
)
and edge set
E
(
F
1
)
∪
E
(
F
2
)
∪
{
x
y
|
x
∈
V
(
F
1
)
and
y
∈
V
(
F
2
)
}
. In this paper, we present a characterization to
(
P
5
,
K
1
∪
K
3
)
-free graphs, prove that
χ
(
G
)
≤
2
ω
(
G
)
-
1
if
G
is
(
P
5
,
K
1
∪
K
3
)
-free. Based on this result, we further prove that
χ
(
G
)
≤
max
{
2
ω
(
G
)
,
15
}
if
G
is a
(
P
5
,
K
1
+
(
K
1
∪
K
3
)
)
-free graph. We also construct a
(
P
5
,
K
1
+
(
K
1
∪
K
3
)
)
-free graph
G
with
χ
(
G
)
=
2
ω
(
G
)
. |
| doi_str_mv | 10.1007/s00373-023-02642-y |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2795520982</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2795520982</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-cbb838b6766aeacf94012f891f2e19d23c321418e57f7ddc2ec3195799ee64bc3</originalsourceid><addsrcrecordid>eNp9kE1OwzAQhS0EEqVwAVaW2LQCg8eOk3hZKlpQy8-irK3EmTSpaFPsZNEbcBaOxUlICRI7FqO3ed8b6SPkHPg1cB7deM5lJBkX-wsDwXYHpAeBVExpCA5Jj2sAxgH0MTnxfsU5VxDwHnkc0UW5LGo6LzeYOHpbNZuM1hWtC6TjwlXrpC4tfWrWKTpa5XTwoq5mcDmYwdfH50wOh2ziEOnUJdvCn5KjPHnzePabffI6uVuM79n8efowHs2ZlaBrZtM0lnEaRmGYYGJzHXAQeawhFwg6E9JKAQHEqKI8yjIrcM-pSGvEMEit7JOLbnfrqvcGfW1WVeM27UsjIq2U4DoWbUt0Lesq7x3mZuvKdeJ2BrjZazOdNtNqMz_azK6FZAf5trxZovub_of6Bq4LbcY</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2795520982</pqid></control><display><type>article</type><title>A Tight Linear Bound to the Chromatic Number of (P5,K1+(K1∪K3))-Free Graphs</title><source>Springer Nature - Complete Springer Journals</source><creator>Dong, Wei ; Xu, Baogang ; Xu, Yian</creator><creatorcontrib>Dong, Wei ; Xu, Baogang ; Xu, Yian</creatorcontrib><description>Let
F
1
and
F
2
be two disjoint graphs. The union
F
1
∪
F
2
is a graph with vertex set
V
(
F
1
)
∪
V
(
F
2
)
and edge set
E
(
F
1
)
∪
E
(
F
2
)
, and the join
F
1
+
F
2
is a graph with vertex set
V
(
F
1
)
∪
V
(
F
2
)
and edge set
E
(
F
1
)
∪
E
(
F
2
)
∪
{
x
y
|
x
∈
V
(
F
1
)
and
y
∈
V
(
F
2
)
}
. In this paper, we present a characterization to
(
P
5
,
K
1
∪
K
3
)
-free graphs, prove that
χ
(
G
)
≤
2
ω
(
G
)
-
1
if
G
is
(
P
5
,
K
1
∪
K
3
)
-free. Based on this result, we further prove that
χ
(
G
)
≤
max
{
2
ω
(
G
)
,
15
}
if
G
is a
(
P
5
,
K
1
+
(
K
1
∪
K
3
)
)
-free graph. We also construct a
(
P
5
,
K
1
+
(
K
1
∪
K
3
)
)
-free graph
G
with
χ
(
G
)
=
2
ω
(
G
)
.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-023-02642-y</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Combinatorics ; Engineering Design ; Graphs ; Mathematics ; Mathematics and Statistics ; Original Paper ; Vertex sets</subject><ispartof>Graphs and combinatorics, 2023-06, Vol.39 (3), Article 43</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. 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><citedby>FETCH-LOGICAL-c319t-cbb838b6766aeacf94012f891f2e19d23c321418e57f7ddc2ec3195799ee64bc3</citedby><cites>FETCH-LOGICAL-c319t-cbb838b6766aeacf94012f891f2e19d23c321418e57f7ddc2ec3195799ee64bc3</cites><orcidid>0000-0002-1424-7042</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/s00373-023-02642-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-023-02642-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Dong, Wei</creatorcontrib><creatorcontrib>Xu, Baogang</creatorcontrib><creatorcontrib>Xu, Yian</creatorcontrib><title>A Tight Linear Bound to the Chromatic Number of (P5,K1+(K1∪K3))-Free Graphs</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>Let
F
1
and
F
2
be two disjoint graphs. The union
F
1
∪
F
2
is a graph with vertex set
V
(
F
1
)
∪
V
(
F
2
)
and edge set
E
(
F
1
)
∪
E
(
F
2
)
, and the join
F
1
+
F
2
is a graph with vertex set
V
(
F
1
)
∪
V
(
F
2
)
and edge set
E
(
F
1
)
∪
E
(
F
2
)
∪
{
x
y
|
x
∈
V
(
F
1
)
and
y
∈
V
(
F
2
)
}
. In this paper, we present a characterization to
(
P
5
,
K
1
∪
K
3
)
-free graphs, prove that
χ
(
G
)
≤
2
ω
(
G
)
-
1
if
G
is
(
P
5
,
K
1
∪
K
3
)
-free. Based on this result, we further prove that
χ
(
G
)
≤
max
{
2
ω
(
G
)
,
15
}
if
G
is a
(
P
5
,
K
1
+
(
K
1
∪
K
3
)
)
-free graph. We also construct a
(
P
5
,
K
1
+
(
K
1
∪
K
3
)
)
-free graph
G
with
χ
(
G
)
=
2
ω
(
G
)
.</description><subject>Combinatorics</subject><subject>Engineering Design</subject><subject>Graphs</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Vertex sets</subject><issn>0911-0119</issn><issn>1435-5914</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE1OwzAQhS0EEqVwAVaW2LQCg8eOk3hZKlpQy8-irK3EmTSpaFPsZNEbcBaOxUlICRI7FqO3ed8b6SPkHPg1cB7deM5lJBkX-wsDwXYHpAeBVExpCA5Jj2sAxgH0MTnxfsU5VxDwHnkc0UW5LGo6LzeYOHpbNZuM1hWtC6TjwlXrpC4tfWrWKTpa5XTwoq5mcDmYwdfH50wOh2ziEOnUJdvCn5KjPHnzePabffI6uVuM79n8efowHs2ZlaBrZtM0lnEaRmGYYGJzHXAQeawhFwg6E9JKAQHEqKI8yjIrcM-pSGvEMEit7JOLbnfrqvcGfW1WVeM27UsjIq2U4DoWbUt0Lesq7x3mZuvKdeJ2BrjZazOdNtNqMz_azK6FZAf5trxZovub_of6Bq4LbcY</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Dong, Wei</creator><creator>Xu, Baogang</creator><creator>Xu, Yian</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/0000-0002-1424-7042</orcidid></search><sort><creationdate>20230601</creationdate><title>A Tight Linear Bound to the Chromatic Number of (P5,K1+(K1∪K3))-Free Graphs</title><author>Dong, Wei ; Xu, Baogang ; Xu, Yian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-cbb838b6766aeacf94012f891f2e19d23c321418e57f7ddc2ec3195799ee64bc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Combinatorics</topic><topic>Engineering Design</topic><topic>Graphs</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Vertex sets</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dong, Wei</creatorcontrib><creatorcontrib>Xu, Baogang</creatorcontrib><creatorcontrib>Xu, Yian</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>Dong, Wei</au><au>Xu, Baogang</au><au>Xu, Yian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Tight Linear Bound to the Chromatic Number of (P5,K1+(K1∪K3))-Free Graphs</atitle><jtitle>Graphs and combinatorics</jtitle><stitle>Graphs and Combinatorics</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>39</volume><issue>3</issue><artnum>43</artnum><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>Let
F
1
and
F
2
be two disjoint graphs. The union
F
1
∪
F
2
is a graph with vertex set
V
(
F
1
)
∪
V
(
F
2
)
and edge set
E
(
F
1
)
∪
E
(
F
2
)
, and the join
F
1
+
F
2
is a graph with vertex set
V
(
F
1
)
∪
V
(
F
2
)
and edge set
E
(
F
1
)
∪
E
(
F
2
)
∪
{
x
y
|
x
∈
V
(
F
1
)
and
y
∈
V
(
F
2
)
}
. In this paper, we present a characterization to
(
P
5
,
K
1
∪
K
3
)
-free graphs, prove that
χ
(
G
)
≤
2
ω
(
G
)
-
1
if
G
is
(
P
5
,
K
1
∪
K
3
)
-free. Based on this result, we further prove that
χ
(
G
)
≤
max
{
2
ω
(
G
)
,
15
}
if
G
is a
(
P
5
,
K
1
+
(
K
1
∪
K
3
)
)
-free graph. We also construct a
(
P
5
,
K
1
+
(
K
1
∪
K
3
)
)
-free graph
G
with
χ
(
G
)
=
2
ω
(
G
)
.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s00373-023-02642-y</doi><orcidid>https://orcid.org/0000-0002-1424-7042</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0911-0119 |
| ispartof | Graphs and combinatorics, 2023-06, Vol.39 (3), Article 43 |
| issn | 0911-0119 1435-5914 |
| language | eng |
| recordid | cdi_proquest_journals_2795520982 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Combinatorics Engineering Design Graphs Mathematics Mathematics and Statistics Original Paper Vertex sets |
| title | A Tight Linear Bound to the Chromatic Number of (P5,K1+(K1∪K3))-Free Graphs |
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