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Improvements on the density of maximal 1-planar graphs

János Barát, Gézá Tóth

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Abstract

Megjegyzés-27402909 N1 Funding details: MTA, Magyar Tudományos Akadémia N1 Funding details: NKFIH K-111827 N1 Funding details: NN-114614 N1 Funding text: Alfréd Rényi, Institute of Math ematics, Hungarian Academy of Sciences, Budapest, Hungary. E mail: toth.geza@renyi.mta.hu Contract grant sponsor: National Research, Development and Innovation Office; contract grant number: NKFIH K-111827. N1 Funding text: Contract grant sponsor: Széchenyi 2020 under the EFOP-3.6.1-16-2016-00015 and OTKA-ARRS Slovenian-Hungarian Joint Research Project; contract grant number: NN-114614. Funding Agency and Grant Number: National Research, Development and Innovation Office [NKFIHK-111827]; Szechenyi [EFOP-3.6.1-16-2016-00015]; OTKA-ARRS Slovenian-Hungarian Joint Research Project [NN-114614] Funding text: Contract grant sponsor: National Research, Development and Innovation Office; contract grant number: NKFIHK-111827.; Contract grant sponsor: Szechenyi 2020 under the EFOP-3.6.1-16-2016-00015 and OTKA-ARRS Slovenian-Hungarian Joint Research Project; contract grant number: NN-114614. Department of Mathematics, University of Pannonia, Veszprém, Hungary MTA-ELTE Geometric and Algebraic Combinatorics Research Group, Eötvös Loránd University, Budapest, Hungary Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary Cited By :1 Export Date: 19 October 2019 CODEN: JGTHD Correspondence Address: Tóth, G.; Alfréd Rényi Institute of Mathematics, Hungarian Academy of SciencesHungary; email: toth.geza@renyi.mta.hu Funding details: Office of Research, Innovation and Economic Development, California State Polytechnic University, Pomona, NKFIH K-111827 Funding details: NN-114614 Funding text 1: Alfréd Rényi, Institute of Math ematics, Hungarian Academy of Sciences, Budapest, Hungary. E mail: toth.geza@renyi.mta.hu Contract grant sponsor: National Research, Development and Innovation Office; contract grant number: NKFIH K-111827. Funding text 2: Contract grant sponsor: Széchenyi 2020 under the EFOP-3.6.1-16-2016-00015 and OTKA-ARRS Slovenian-Hungarian Joint Research Project; contract grant number: NN-114614.

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Megjegyzés-27402909 N1 Funding details: MTA, Magyar Tudományos Akadémia N1 Funding details: NKFIH K-111827 N1 Funding details: NN-114614 N1 Funding text: Alfréd Rényi, Institute of Math ematics, Hungarian Academy of Sciences, Budapest, Hungary. E mail: toth.geza@renyi.mta.hu Contract grant sponsor: National Research, Development and Innovation Office; contract grant number: NKFIH K-111827. N1 Funding text: Contract grant sponsor: Széchenyi 2020 under the EFOP-3.6.1-16-2016-00015 and OTKA-ARRS Slovenian-Hungarian Joint Research Project; contract grant number: NN-114614. Funding Agency and Grant Number: National Research, Development and Innovation Office [NKFIHK-111827]; Szechenyi [EFOP-3.6.1-16-2016-00015]; OTKA-ARRS Slovenian-Hungarian Joint Research Project [NN-114614] Funding text: Contract grant sponsor: National Research, Development and Innovation Office; contract grant number: NKFIHK-111827.; Contract grant sponsor: Szechenyi 2020 under the EFOP-3.6.1-16-2016-00015 and OTKA-ARRS Slovenian-Hungarian Joint Research Project; contract grant number: NN-114614. Department of Mathematics, University of Pannonia, Veszprém, Hungary MTA-ELTE Geometric and Algebraic Combinatorics Research Group, Eötvös Loránd University, Budapest, Hungary Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary Cited By :1 Export Date: 19 October 2019 CODEN: JGTHD Correspondence Address: Tóth, G.; Alfréd Rényi Institute of Mathematics, Hungarian Academy of SciencesHungary; email: toth.geza@renyi.mta.hu Funding details: Office of Research, Innovation and Economic Development, California State Polytechnic University, Pomona, NKFIH K-111827 Funding details: NN-114614 Funding text 1: Alfréd Rényi, Institute of Math ematics, Hungarian Academy of Sciences, Budapest, Hungary. E mail: toth.geza@renyi.mta.hu Contract grant sponsor: National Research, Development and Innovation Office; contract grant number: NKFIH K-111827. Funding text 2: Contract grant sponsor: Széchenyi 2020 under the EFOP-3.6.1-16-2016-00015 and OTKA-ARRS Slovenian-Hungarian Joint Research Project; contract grant number: NN-114614.

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Available abstract

Megjegyzés-27402909 N1 Funding details: MTA, Magyar Tudományos Akadémia N1 Funding details: NKFIH K-111827 N1 Funding details: NN-114614 N1 Funding text: Alfréd Rényi, Institute of Math ematics, Hungarian Academy of Sciences, Budapest, Hungary. E mail: toth.geza@renyi.mta.hu Contract grant sponsor: National Research, Development and Innovation Office; contract grant number: NKFIH K-111827. N1 Funding text: Contract grant sponsor: Széchenyi 2020 under the EFOP-3.6.1-16-2016-00015 and OTKA-ARRS Slovenian-Hungarian Joint Research Project; contract grant number: NN-114614. Funding Agency and Grant Number: National Research, Development and Innovation Office [NKFIHK-111827]; Szechenyi [EFOP-3.6.1-16-2016-00015]; OTKA-ARRS Slovenian-Hungarian Joint Research Project [NN-114614] Funding text: Contract grant sponsor: National Research, Development and Innovation Office; contract grant number: NKFIHK-111827.; Contract grant sponsor: Szechenyi 2020 under the EFOP-3.6.1-16-2016-00015 and OTKA-ARRS Slovenian-Hungarian Joint Research Project; contract grant number: NN-114614. Department of Mathematics, University of Pannonia, Veszprém, Hungary MTA-ELTE Geometric and Algebraic Combinatorics Research Group, Eötvös Loránd University, Budapest, Hungary Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary Cited By :1 Export Date: 19 October 2019 CODEN: JGTHD Correspondence Address: Tóth, G.; Alfréd Rényi Institute of Mathematics, Hungarian Academy of SciencesHungary; email: toth.geza@renyi.mta.hu Funding details: Office of Research, Innovation and Economic Development, California State Polytechnic University, Pomona, NKFIH K-111827 Funding details: NN-114614 Funding text 1: Alfréd Rényi, Institute of Math ematics, Hungarian Academy of Sciences, Budapest, Hungary. E mail: toth.geza@renyi.mta.hu Contract grant sponsor: National Research, Development and Innovation Office; contract grant number: NKFIH K-111827. Funding text 2: Contract grant sponsor: Széchenyi 2020 under the EFOP-3.6.1-16-2016-00015 and OTKA-ARRS Slovenian-Hungarian Joint Research Project; contract grant number: NN-114614.

Key concepts: Planar graph, Combinatorics, Outerplanar graph, Mathematics, Polyhedral graph, Planar straight-line graph, 1-planar graph, Book embedding

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