Exact leaf powers
We define and study the new notion of exact k -leaf powers where a graph G = ( V G , E G ) is an exact k -leaf power if and only if there exists a tree T = ( V T , E T ) — an exact k -leaf root of G — whose set of leaves equals V G such that u v ∈ E G holds for u , v ∈ V G if and only if the distanc...
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| Veröffentlicht in: | Theoretical computer science 2010-06, Vol.411 (31), p.2968-2977 |
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| container_title | Theoretical computer science |
| container_volume | 411 |
| creator | Brandstädt, Andreas Le, Van Bang Rautenbach, Dieter |
| description | We define and study the new notion of exact
k
-leaf powers where a graph
G
=
(
V
G
,
E
G
)
is an exact
k
-leaf power if and only if there exists a tree
T
=
(
V
T
,
E
T
)
— an exact
k
-leaf root of
G
— whose set of leaves equals
V
G
such that
u
v
∈
E
G
holds for
u
,
v
∈
V
G
if and only if the distance of
u
and
v
in
T
is exactly
k
. This new notion is closely related to but different from leaf powers and neighbourhood subtree tolerance graphs.
We prove characterizations of exact
3
- and
4
-leaf powers which imply that such graphs can be recognized in linear time and that also the corresponding exact leaf roots can be found in linear time. Furthermore, we characterize all exact
5
-leaf roots of chordless cycles and derive several properties of exact
5
-leaf powers. |
| doi_str_mv | 10.1016/j.tcs.2010.04.027 |
| format | Article |
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k
-leaf powers where a graph
G
=
(
V
G
,
E
G
)
is an exact
k
-leaf power if and only if there exists a tree
T
=
(
V
T
,
E
T
)
— an exact
k
-leaf root of
G
— whose set of leaves equals
V
G
such that
u
v
∈
E
G
holds for
u
,
v
∈
V
G
if and only if the distance of
u
and
v
in
T
is exactly
k
. This new notion is closely related to but different from leaf powers and neighbourhood subtree tolerance graphs.
We prove characterizations of exact
3
- and
4
-leaf powers which imply that such graphs can be recognized in linear time and that also the corresponding exact leaf roots can be found in linear time. Furthermore, we characterize all exact
5
-leaf roots of chordless cycles and derive several properties of exact
5
-leaf powers.</description><identifier>ISSN: 0304-3975</identifier><identifier>EISSN: 1879-2294</identifier><identifier>DOI: 10.1016/j.tcs.2010.04.027</identifier><identifier>CODEN: TCSCDI</identifier><language>eng</language><publisher>Oxford: Elsevier B.V</publisher><subject>Applied sciences ; C (programming language) ; Combinatorics ; Combinatorics. Ordered structures ; Computer science; control theory; systems ; Exact sciences and technology ; Forbidden induced subgraph ; Graph power ; Graph theory ; Graphs ; Information retrieval. Graph ; Leaf power ; Leaf root ; Leaves ; Mathematics ; Miscellaneous ; Phylogenetic tree ; Phylogeny ; Roots ; Sciences and techniques of general use ; Theoretical computing ; Tolerances ; Trees</subject><ispartof>Theoretical computer science, 2010-06, Vol.411 (31), p.2968-2977</ispartof><rights>2010 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-37939db51fdd1991bb263dc6758a2deb3e8e6451dd8452267b275a572e0ccb3a3</citedby><cites>FETCH-LOGICAL-c360t-37939db51fdd1991bb263dc6758a2deb3e8e6451dd8452267b275a572e0ccb3a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.tcs.2010.04.027$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>315,781,785,3551,27928,27929,45999</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22895662$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Brandstädt, Andreas</creatorcontrib><creatorcontrib>Le, Van Bang</creatorcontrib><creatorcontrib>Rautenbach, Dieter</creatorcontrib><title>Exact leaf powers</title><title>Theoretical computer science</title><description>We define and study the new notion of exact
k
-leaf powers where a graph
G
=
(
V
G
,
E
G
)
is an exact
k
-leaf power if and only if there exists a tree
T
=
(
V
T
,
E
T
)
— an exact
k
-leaf root of
G
— whose set of leaves equals
V
G
such that
u
v
∈
E
G
holds for
u
,
v
∈
V
G
if and only if the distance of
u
and
v
in
T
is exactly
k
. This new notion is closely related to but different from leaf powers and neighbourhood subtree tolerance graphs.
We prove characterizations of exact
3
- and
4
-leaf powers which imply that such graphs can be recognized in linear time and that also the corresponding exact leaf roots can be found in linear time. Furthermore, we characterize all exact
5
-leaf roots of chordless cycles and derive several properties of exact
5
-leaf powers.</description><subject>Applied sciences</subject><subject>C (programming language)</subject><subject>Combinatorics</subject><subject>Combinatorics. Ordered structures</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Forbidden induced subgraph</subject><subject>Graph power</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Information retrieval. Graph</subject><subject>Leaf power</subject><subject>Leaf root</subject><subject>Leaves</subject><subject>Mathematics</subject><subject>Miscellaneous</subject><subject>Phylogenetic tree</subject><subject>Phylogeny</subject><subject>Roots</subject><subject>Sciences and techniques of general use</subject><subject>Theoretical computing</subject><subject>Tolerances</subject><subject>Trees</subject><issn>0304-3975</issn><issn>1879-2294</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9j01LAzEQhoMoWKsHj956Ebzsmkw2yQZPUuoHFLzoOWSTWUjZdmuy9ePfN2WLR-cyDDzvOzyE3DBaMsrk_aocXCqB5ptWJQV1QiasVroA0NUpmVBOq4JrJc7JRUormkcoOSHXix_rhlmHtp1t-2-M6ZKctbZLeHXcU_LxtHifvxTLt-fX-eOycFzSoeBKc-0bwVrvmdasaUBy76QStQWPDccaZSWY93UlAKRqQAkrFCB1ruGWT8nd2LuN_ecO02DWITnsOrvBfpcMk4oBCM3rjLIRdbFPKWJrtjGsbfw1jJqDvlmZrG8O-oZWJuvnzO2x3iZnuzbajQvpLwhQayElZO5h5DC7fgWMJrmAG4c-RHSD8X3458se785s-g</recordid><startdate>20100628</startdate><enddate>20100628</enddate><creator>Brandstädt, Andreas</creator><creator>Le, Van Bang</creator><creator>Rautenbach, Dieter</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20100628</creationdate><title>Exact leaf powers</title><author>Brandstädt, Andreas ; Le, Van Bang ; Rautenbach, Dieter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-37939db51fdd1991bb263dc6758a2deb3e8e6451dd8452267b275a572e0ccb3a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Applied sciences</topic><topic>C (programming language)</topic><topic>Combinatorics</topic><topic>Combinatorics. Ordered structures</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Forbidden induced subgraph</topic><topic>Graph power</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Information retrieval. Graph</topic><topic>Leaf power</topic><topic>Leaf root</topic><topic>Leaves</topic><topic>Mathematics</topic><topic>Miscellaneous</topic><topic>Phylogenetic tree</topic><topic>Phylogeny</topic><topic>Roots</topic><topic>Sciences and techniques of general use</topic><topic>Theoretical computing</topic><topic>Tolerances</topic><topic>Trees</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Brandstädt, Andreas</creatorcontrib><creatorcontrib>Le, Van Bang</creatorcontrib><creatorcontrib>Rautenbach, Dieter</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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>Theoretical computer science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Brandstädt, Andreas</au><au>Le, Van Bang</au><au>Rautenbach, Dieter</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact leaf powers</atitle><jtitle>Theoretical computer science</jtitle><date>2010-06-28</date><risdate>2010</risdate><volume>411</volume><issue>31</issue><spage>2968</spage><epage>2977</epage><pages>2968-2977</pages><issn>0304-3975</issn><eissn>1879-2294</eissn><coden>TCSCDI</coden><abstract>We define and study the new notion of exact
k
-leaf powers where a graph
G
=
(
V
G
,
E
G
)
is an exact
k
-leaf power if and only if there exists a tree
T
=
(
V
T
,
E
T
)
— an exact
k
-leaf root of
G
— whose set of leaves equals
V
G
such that
u
v
∈
E
G
holds for
u
,
v
∈
V
G
if and only if the distance of
u
and
v
in
T
is exactly
k
. This new notion is closely related to but different from leaf powers and neighbourhood subtree tolerance graphs.
We prove characterizations of exact
3
- and
4
-leaf powers which imply that such graphs can be recognized in linear time and that also the corresponding exact leaf roots can be found in linear time. Furthermore, we characterize all exact
5
-leaf roots of chordless cycles and derive several properties of exact
5
-leaf powers.</abstract><cop>Oxford</cop><pub>Elsevier B.V</pub><doi>10.1016/j.tcs.2010.04.027</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0304-3975 |
| ispartof | Theoretical computer science, 2010-06, Vol.411 (31), p.2968-2977 |
| issn | 0304-3975 1879-2294 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1671225938 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Access via ScienceDirect (Elsevier) |
| subjects | Applied sciences C (programming language) Combinatorics Combinatorics. Ordered structures Computer science control theory systems Exact sciences and technology Forbidden induced subgraph Graph power Graph theory Graphs Information retrieval. Graph Leaf power Leaf root Leaves Mathematics Miscellaneous Phylogenetic tree Phylogeny Roots Sciences and techniques of general use Theoretical computing Tolerances Trees |
| title | Exact leaf powers |
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