Zip product of graphs and crossing numbers
D. Bokal proved that the crossing number is additive for the zip product under the condition of having two coherent bundles in the zipped graphs. This property is very effective when dealing with the crossing numbers of (capped) Cartesian product of trees with graphs containing a dominating vertex....
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| Veröffentlicht in: | Journal of graph theory 2021-02, Vol.96 (2), p.289-309 |
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| container_title | Journal of graph theory |
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| creator | Ouyang, Zhangdong Huang, Yuanqiu Dong, Fengming Tay, Eng Guan |
| description | D. Bokal proved that the crossing number is additive for the zip product under the condition of having two coherent bundles in the zipped graphs. This property is very effective when dealing with the crossing numbers of (capped) Cartesian product of trees with graphs containing a dominating vertex. In this paper, we first prove that the crossing number is still additive for the zip product under a weaker condition. Based on the new condition, we then establish some general expressions for bounding the crossing numbers of (capped) Cartesian product of trees with graphs (possibly without dominating vertex). Exact values of the crossing numbers of Cartesian product of trees with most graphs of order at most five are obtained by applying these expressions, which extend some previous results due to M. Klešč. In fact, our results can also be applied to deal with Cartesian product of trees with graphs of order more than five. |
| doi_str_mv | 10.1002/jgt.22613 |
| format | Article |
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Bokal proved that the crossing number is additive for the zip product under the condition of having two coherent bundles in the zipped graphs. This property is very effective when dealing with the crossing numbers of (capped) Cartesian product of trees with graphs containing a dominating vertex. In this paper, we first prove that the crossing number is still additive for the zip product under a weaker condition. Based on the new condition, we then establish some general expressions for bounding the crossing numbers of (capped) Cartesian product of trees with graphs (possibly without dominating vertex). Exact values of the crossing numbers of Cartesian product of trees with most graphs of order at most five are obtained by applying these expressions, which extend some previous results due to M. Klešč. 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Bokal proved that the crossing number is additive for the zip product under the condition of having two coherent bundles in the zipped graphs. This property is very effective when dealing with the crossing numbers of (capped) Cartesian product of trees with graphs containing a dominating vertex. In this paper, we first prove that the crossing number is still additive for the zip product under a weaker condition. Based on the new condition, we then establish some general expressions for bounding the crossing numbers of (capped) Cartesian product of trees with graphs (possibly without dominating vertex). Exact values of the crossing numbers of Cartesian product of trees with most graphs of order at most five are obtained by applying these expressions, which extend some previous results due to M. Klešč. In fact, our results can also be applied to deal with Cartesian product of trees with graphs of order more than five.</description><subject>Cartesian coordinates</subject><subject>Cartesian product</subject><subject>crossing number</subject><subject>Graphs</subject><subject>tree</subject><subject>Trees</subject><subject>Trees (mathematics)</subject><subject>zip product</subject><issn>0364-9024</issn><issn>1097-0118</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kMFOwzAMhiMEEmNw4A0qcQKpW-K0SXNEExugSVzGhUuUpm5ptbUlaYX29oSVKydL1mf790fILaMLRiksm2pYAAjGz8iMUSVjylh2TmaUiyRWFJJLcuV9Q0M7pdmMPHzUfdS7rhjtEHVlVDnTf_rItEVkXed93VZROx5ydP6aXJRm7_Hmr87J-_ppt3qOt2-bl9XjNragJI-FyjHnxtoCkgSt5CkiZJikEkpjJSoJKi9QgjA0pcgBc-BWZsByi6USfE7upr0h1teIftBNN7o2nNSQCCl4eEUG6n6iTjEdlrp39cG4o2ZU_6rQQYU-qQjscmK_6z0e_wf162Y3TfwAlZ9e2w</recordid><startdate>202102</startdate><enddate>202102</enddate><creator>Ouyang, Zhangdong</creator><creator>Huang, Yuanqiu</creator><creator>Dong, Fengming</creator><creator>Tay, Eng Guan</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-5389-6221</orcidid><orcidid>https://orcid.org/0000-0002-6081-6293</orcidid><orcidid>https://orcid.org/0000-0002-8510-2262</orcidid><orcidid>https://orcid.org/0000-0003-1559-8909</orcidid></search><sort><creationdate>202102</creationdate><title>Zip product of graphs and crossing numbers</title><author>Ouyang, Zhangdong ; Huang, Yuanqiu ; Dong, Fengming ; Tay, Eng Guan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2973-69beb3accd244ec735ee28e4572fac7e9729bde726a050e32eb23c7821bcef963</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Cartesian coordinates</topic><topic>Cartesian product</topic><topic>crossing number</topic><topic>Graphs</topic><topic>tree</topic><topic>Trees</topic><topic>Trees (mathematics)</topic><topic>zip product</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ouyang, Zhangdong</creatorcontrib><creatorcontrib>Huang, Yuanqiu</creatorcontrib><creatorcontrib>Dong, Fengming</creatorcontrib><creatorcontrib>Tay, Eng Guan</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of graph theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ouyang, Zhangdong</au><au>Huang, Yuanqiu</au><au>Dong, Fengming</au><au>Tay, Eng Guan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Zip product of graphs and crossing numbers</atitle><jtitle>Journal of graph theory</jtitle><date>2021-02</date><risdate>2021</risdate><volume>96</volume><issue>2</issue><spage>289</spage><epage>309</epage><pages>289-309</pages><issn>0364-9024</issn><eissn>1097-0118</eissn><abstract>D. Bokal proved that the crossing number is additive for the zip product under the condition of having two coherent bundles in the zipped graphs. This property is very effective when dealing with the crossing numbers of (capped) Cartesian product of trees with graphs containing a dominating vertex. In this paper, we first prove that the crossing number is still additive for the zip product under a weaker condition. Based on the new condition, we then establish some general expressions for bounding the crossing numbers of (capped) Cartesian product of trees with graphs (possibly without dominating vertex). Exact values of the crossing numbers of Cartesian product of trees with most graphs of order at most five are obtained by applying these expressions, which extend some previous results due to M. Klešč. 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| subjects | Cartesian coordinates Cartesian product crossing number Graphs tree Trees Trees (mathematics) zip product |
| title | Zip product of graphs and crossing numbers |
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