The relation between the number of leaves of a tree and its diameter
Let L ( n, d ) denote the minimum possible number of leaves in a tree of order n and diameter d . Lesniak (1975) gave the lower bound B ( n,d ) = ⌈2( n − 1)/ d ⌉ for L ( n,d ). When d is even, B ( n,d ) = L ( n,d ). But when d is odd, B ( n,d ) is smaller than L ( n,d ) in general. For example, B (2...
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| Veröffentlicht in: | Czechoslovak Mathematical Journal 2022, Vol.72 (2), p.365-369 |
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| container_title | Czechoslovak Mathematical Journal |
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| creator | Qiao, Pu Zhan, Xingzhi |
| description | Let
L
(
n, d
) denote the minimum possible number of leaves in a tree of order
n
and diameter
d
. Lesniak (1975) gave the lower bound
B
(
n,d
) = ⌈2(
n
− 1)/
d
⌉ for
L
(
n,d
). When
d
is even,
B
(
n,d
) =
L
(
n,d
). But when
d
is odd,
B
(
n,d
) is smaller than
L
(
n,d
) in general. For example,
B
(21, 3) = 14 while
L
(21, 3) = 19. In this note, we determine
L
(
n, d
) using new ideas. We also consider the converse problem and determine the minimum possible diameter of a tree with given order and number of leaves. |
| doi_str_mv | 10.21136/CMJ.2021.0492-20 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2655589177</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2655589177</sourcerecordid><originalsourceid>FETCH-LOGICAL-c359t-8cd54412756ad9c3117a9f964312cf5dfaa015ec53363862807e3af7d262533d3</originalsourceid><addsrcrecordid>eNp1kEtLAzEUhYMoWKs_wF3A9dTcPGeWUt9U3NR1SCc3OqWdqUmq-O9NreDK1T0czjkXPkLOgU04gNCX06fHCWccJkw2vOLsgIxAGV41IOGQjBgDqKSW_JicpLRkjAmQ9Yhcz9-QRly53A09XWD-ROxpLma_XS8w0iHQFboPTDvlaI6I1PWedjlR37k1Zoyn5Ci4VcKz3zsmL7c38-l9NXu-e5hezapWqCZXdeuVlMCN0s43rQAwrgmNlgJ4G5QPzjFQ2CohtKg1r5lB4YLxXPPieTEmF_vdTRzet5iyXQ7b2JeXlmulVN2AMSUF-1Qbh5QiBruJ3drFLwvM_sCyBZbdwbI7WEWVDt93Usn2rxj_lv8vfQMyL2os</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2655589177</pqid></control><display><type>article</type><title>The relation between the number of leaves of a tree and its diameter</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Alma/SFX Local Collection</source><source>SpringerLink Journals - AutoHoldings</source><creator>Qiao, Pu ; Zhan, Xingzhi</creator><creatorcontrib>Qiao, Pu ; Zhan, Xingzhi</creatorcontrib><description>Let
L
(
n, d
) denote the minimum possible number of leaves in a tree of order
n
and diameter
d
. Lesniak (1975) gave the lower bound
B
(
n,d
) = ⌈2(
n
− 1)/
d
⌉ for
L
(
n,d
). When
d
is even,
B
(
n,d
) =
L
(
n,d
). But when
d
is odd,
B
(
n,d
) is smaller than
L
(
n,d
) in general. For example,
B
(21, 3) = 14 while
L
(21, 3) = 19. In this note, we determine
L
(
n, d
) using new ideas. We also consider the converse problem and determine the minimum possible diameter of a tree with given order and number of leaves.</description><identifier>ISSN: 0011-4642</identifier><identifier>EISSN: 1572-9141</identifier><identifier>DOI: 10.21136/CMJ.2021.0492-20</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Convex and Discrete Geometry ; Lower bounds ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations</subject><ispartof>Czechoslovak Mathematical Journal, 2022, Vol.72 (2), p.365-369</ispartof><rights>Institute of Mathematics, Czech Academy of Sciences 2021</rights><rights>Institute of Mathematics, Czech Academy of Sciences 2021.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-8cd54412756ad9c3117a9f964312cf5dfaa015ec53363862807e3af7d262533d3</citedby><cites>FETCH-LOGICAL-c359t-8cd54412756ad9c3117a9f964312cf5dfaa015ec53363862807e3af7d262533d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.21136/CMJ.2021.0492-20$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.21136/CMJ.2021.0492-20$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Qiao, Pu</creatorcontrib><creatorcontrib>Zhan, Xingzhi</creatorcontrib><title>The relation between the number of leaves of a tree and its diameter</title><title>Czechoslovak Mathematical Journal</title><addtitle>Czech Math J</addtitle><description>Let
L
(
n, d
) denote the minimum possible number of leaves in a tree of order
n
and diameter
d
. Lesniak (1975) gave the lower bound
B
(
n,d
) = ⌈2(
n
− 1)/
d
⌉ for
L
(
n,d
). When
d
is even,
B
(
n,d
) =
L
(
n,d
). But when
d
is odd,
B
(
n,d
) is smaller than
L
(
n,d
) in general. For example,
B
(21, 3) = 14 while
L
(21, 3) = 19. In this note, we determine
L
(
n, d
) using new ideas. We also consider the converse problem and determine the minimum possible diameter of a tree with given order and number of leaves.</description><subject>Analysis</subject><subject>Convex and Discrete Geometry</subject><subject>Lower bounds</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><issn>0011-4642</issn><issn>1572-9141</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLAzEUhYMoWKs_wF3A9dTcPGeWUt9U3NR1SCc3OqWdqUmq-O9NreDK1T0czjkXPkLOgU04gNCX06fHCWccJkw2vOLsgIxAGV41IOGQjBgDqKSW_JicpLRkjAmQ9Yhcz9-QRly53A09XWD-ROxpLma_XS8w0iHQFboPTDvlaI6I1PWedjlR37k1Zoyn5Ci4VcKz3zsmL7c38-l9NXu-e5hezapWqCZXdeuVlMCN0s43rQAwrgmNlgJ4G5QPzjFQ2CohtKg1r5lB4YLxXPPieTEmF_vdTRzet5iyXQ7b2JeXlmulVN2AMSUF-1Qbh5QiBruJ3drFLwvM_sCyBZbdwbI7WEWVDt93Usn2rxj_lv8vfQMyL2os</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Qiao, Pu</creator><creator>Zhan, Xingzhi</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2022</creationdate><title>The relation between the number of leaves of a tree and its diameter</title><author>Qiao, Pu ; Zhan, Xingzhi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-8cd54412756ad9c3117a9f964312cf5dfaa015ec53363862807e3af7d262533d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Analysis</topic><topic>Convex and Discrete Geometry</topic><topic>Lower bounds</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Qiao, Pu</creatorcontrib><creatorcontrib>Zhan, Xingzhi</creatorcontrib><collection>CrossRef</collection><jtitle>Czechoslovak Mathematical Journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Qiao, Pu</au><au>Zhan, Xingzhi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The relation between the number of leaves of a tree and its diameter</atitle><jtitle>Czechoslovak Mathematical Journal</jtitle><stitle>Czech Math J</stitle><date>2022</date><risdate>2022</risdate><volume>72</volume><issue>2</issue><spage>365</spage><epage>369</epage><pages>365-369</pages><issn>0011-4642</issn><eissn>1572-9141</eissn><abstract>Let
L
(
n, d
) denote the minimum possible number of leaves in a tree of order
n
and diameter
d
. Lesniak (1975) gave the lower bound
B
(
n,d
) = ⌈2(
n
− 1)/
d
⌉ for
L
(
n,d
). When
d
is even,
B
(
n,d
) =
L
(
n,d
). But when
d
is odd,
B
(
n,d
) is smaller than
L
(
n,d
) in general. For example,
B
(21, 3) = 14 while
L
(21, 3) = 19. In this note, we determine
L
(
n, d
) using new ideas. We also consider the converse problem and determine the minimum possible diameter of a tree with given order and number of leaves.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.21136/CMJ.2021.0492-20</doi><tpages>5</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0011-4642 |
| ispartof | Czechoslovak Mathematical Journal, 2022, Vol.72 (2), p.365-369 |
| issn | 0011-4642 1572-9141 |
| language | eng |
| recordid | cdi_proquest_journals_2655589177 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection; SpringerLink Journals - AutoHoldings |
| subjects | Analysis Convex and Discrete Geometry Lower bounds Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Ordinary Differential Equations |
| title | The relation between the number of leaves of a tree and its diameter |
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