LEADER 03578nam 22006255 450 001 9910254071403321 005 20220413214931.0 010 $a3-319-31951-5 024 7 $a10.1007/978-3-319-31951-3 035 $a(CKB)3710000000685963 035 $a(EBL)4529717 035 $a(DE-He213)978-3-319-31951-3 035 $a(MiAaPQ)EBC4529717 035 $a(PPN)194077853 035 $a(EXLCZ)993710000000685963 100 $a20160518d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPancyclic and bipancyclic graphs /$fby John C. George, Abdollah Khodkar, W.D. Wallis 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (117 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 $a3-319-31950-7 320 $aIncludes bibliographical references. 327 $a1.Graphs -- 2. Degrees and Hamiltoneity -- 3. Pancyclicity -- 4. Minimal Pancyclicity -- 5. Uniquely Pancyclic Graphs -- 6. Bipancyclic Graphs -- 7. Uniquely Bipancyclic Graphs -- 8. Minimal Bipancyclicity -- References. . 330 $aThis book is focused on pancyclic and bipancyclic graphs and is geared toward researchers and graduate students in graph theory. Readers should be familiar with the basic concepts of graph theory, the definitions of a graph and of a cycle. Pancyclic graphs contain cycles of all possible lengths from three up to the number of vertices in the graph. Bipartite graphs contain only cycles of even lengths, a bipancyclic graph is defined to be a bipartite graph with cycles of every even size from 4 vertices up to the number of vertices in the graph. Cutting edge research and fundamental results on pancyclic and bipartite graphs from a wide range of journal articles and conference proceedings are composed in this book to create a standalone presentation. The following questions are highlighted through the book: - What is the smallest possible number of edges in a pancyclic graph with v vertices? - When do pancyclic graphs exist with exactly one cycle of every possible length? - What is the smallest possible number of edges in a bipartite graph with v vertices? - When do bipartite graphs exist with exactly one cycle of every possible length? 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aGraph theory 606 $aCombinatorics 606 $aNumerical analysis 606 $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aGraph theory. 615 0$aCombinatorics. 615 0$aNumerical analysis. 615 14$aGraph Theory. 615 24$aCombinatorics. 615 24$aNumerical Analysis. 676 $a511.5 700 $aGeorge$b John C$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756032 702 $aKhodkar$b Abdollah$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWallis$b W.D$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254071403321 996 $aPancyclic and Bipancyclic Graphs$92162746 997 $aUNINA