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Graham R.L., Grotschel M., Lovasz L. — Handbook of combinatorics (vol. 1)
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Íàçâàíèå: Handbook of combinatorics (vol. 1)Àâòîðû: Graham R.L., Grotschel M., Lovasz L.Àííîòàöèÿ: Combinatorics research, the branch of mathematics that deals with the study of discrete, usually finite, structures, covers a wide range of problems not only in mathematics but also in the biological sciences, engineering, and computer science. The Handbook of Combinatorics brings together almost every aspect of this enormous field and is destined to become a classic. Ronald L. Graham, Martin Grotschel, and Laszlo Lovasz, three of the world's leading combinatorialists, have compiled a selection of articles that cover combinatorics in graph theory, theoretical computer science, optimization, and convexity theory, plus applications in operations research, electrical engineering, statistical mechanics, chemistry, molecular biology, pure mathematics, and computer science.
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Out-of-kilter method 1581 Outcome 2123 Outdegree 15 Outerplanar graph 308 Output gate 2012 Oval 658 683 Overhagen, I. 950 Overlap graph 58 Overlapping bridges 58 Ovoid 675 Oxley, J.G. 491 501 505 S08 516 522 523 535 540 1931 2178 Oxley, J.G.A. 516; see “Brylawski T.H.” Oxtoby, J.C. 1474 Ozanam, J. 2168 Ozawa, T. 1921 O’Brien, E.A. 1484; see “Celler F.” O’Brien, R.C. 87 O’Keefe, E.S. 709 O’Nan, M.E. 631 O’Nan-Scott theorem 617 656 P-geometry 683 P-polynomial scheme 761 P-recursive sequences 1109 P-saturated 1268 p-vector 909 Pach, J. 854; see “Barany I.” Pach, J.A. 836; see “Erdos P.” Pach, J.B. 1236 1522 1721 1722 1725; P.” Pach, J.C. 1578; see “Kotnlos J.” Pach, J.D. 1357; see “Laimann D.” Pach, J.E. 811; see “Moser W.O.J.” Pachner, U. 1857 Pachner, U.A, 879; see “Ewald G.” Pack, I.; see Avis, D. 837 Packing 80 142 404 776 934 1276 Packing constant 935 Packing density 935 Packing graphs 1276 Packing trees 1280 Padberg, M. 1573; see “Hofrman K.L.” Padberg, M.W.A. 131 132 207 268 1571—1573 1658 1662 1667 1680 1681 1695 1696 1881 2188 Padberg, M.W.B. 1696; see “Balas E.” Padberg, M.W.C. 1696; see “Crowder H.” Padberg, M.W.D. 1573 1654 1696; M.” Pairing theorem 1957 1972 Pairwise balanced design see “PBD” Palasti, I. 820 822 Palasti, I.A. 818 821 823; Z.” Paley graphs 1760 1761 Paley matrix 795 Paley, R.E.A.C. 730 753 2183 Palfy, P.P. 1516 Palfy, P.P.A. 1460 1516; L.” Palfy, P.P.B. 1520; see “Babai L.” Palka, Z. 370 Palmer, E. 1060; see “Harary F.” Palmer, E.M. 354 Palmer, E.M.A. 1162 1195 1213; F.” Panconnected graph 78 Pancyclic graph 24 25 Pancyclic oirlering 78 Pancyclic vertex 32 Pannwitz, E. 836 Papadimilricu, C.H.B. 1557 1888; D.S.” Papadimitricu, C.H.A. 183 1659 1693 1696 Papadimitricu, C.H.C. 1662 1693; R.M.” Papadimitricu, C.H.D. 1903 1904; A.W.J.” Papernov, B.A. 163 Pappus configuration 813 Pappus theorem 652 653 Parallel algorithm 1642 Parallel class 705 Parallel computation 1637 1640 Parallel elements of a matroid 490 498 Parallelism 655 1544 Parallelotopes 853 858 921 944 945 Parameter sets 1360 1362 Parent 13 Paris, J. 1353 Paris, J.A. 1356; see “Kirby L.” Paris, L. 2070 Parisi, O. 1947; see “Mezard M.” Parity check 777 Parity function 1625 1626 1803 1806 2013 2016 Parity gates 2013 Parity of a walk 9 Parity polynomial-time hierarchy 1626 Parker, E.T. 697 2183 Parker, E.T.A. 705 707 2183.; R.C.” Parker, R.A 622.; see “Conway J.H.” Parsons, T.D. 60; see “Jackson B.” Parsons, T.D.A. 1474; see “Marusic D.” Part, J. 844 846 865 Parthasarathy, K.R. 268 Partial (sub)hypergraph 386 Partial geometry 684 Partial hypergraph 401 408 Partial k-coloring 49 Partial k-path partition 50 Partial l-design 1306 Partial linear space 668 696 Partial order 435 Partial representation (PR) 584 Partial transversal 186 500 501 2178 Partially balanced incomplete block design see “PBIBD” Partially ordered sets see “Posets” Partite construction 1381 1391 Partite lemma 1390 Partite system 1389 Partition 80 426 1037 1056 1068 1727 2168 2172 Partition (vertex partition) 81 Partition function 1927 1930 1941 1944 1949 Partition lattice 444 446 Partition of a graph 43 1830 Partition of integers 2167 Partition regular 1358 Partition-generating function 2168 Partitionable 561 Partitions with bounded part sizes 1164 Partizan games 2127 2145 2150 2158 Pascal, B. 2166 2167 Pascal’s triangle 2166 Pasini, A. 683; see “Cameron P.J.” Pasini, A.A. 683; see “Del Fra A.” Pasquier, G. 791 Patashnik, O. 1071 1073 1090 1131 1132 1212; R.L.” Path 9 114 391 400 1472 Path (in a hypergraph) 387 Path compression 2025 2026 Path decomposition 86 Path double cover 93 Path partition of a graph 43 Path system 26 Path width 337 Path-tough graph 53 Patterson, S.J. 958 Paturi, R. 1765 Paul, W. 1629; see Hopcroft J. Paul, W.J. 1629 1754 Paving 498 Paving matroid 499 Pavlov, A.I. 1126 Payan, C. 416; see “Jaeger F.” Payan, C.A. 49; see “Laborde J.M.” Payne, S.E. 676 PBD (pairwise balanced design) 696 PBD-closed set 707 PBIBD (partially balanced incomplete block design) 706 Peano arithmetic 1352 Peck, G.W. 474 475 Pedoe, D. 889; see “Hodge W.V.D.” Peled, U.N. 1696; see “Hammer P.L.” Pellegrino, G. 661 Peltesohn, R. 709 Pen-strokes 2176 Penn, M. 165; see “Korach E.” Penrice, S. 443; see “Kierstead H.” Penrice, S.G. 1209 Penttila, T. 656 Percolation 1932 Percolation methods 1210 Percolation theory 1933 Percus, J.K. 1941 1944 Peresy, N. 666 Perfect 2-matching 219 264 Perfect and extreme forms 958 Perfect codes 717 778 802 804 Perfect graphs 182 265—267 269 270 1546 1591 1687 Perfect matching 46 181 410 1579 1588 1590 1627 1628 2016 2052 2186 Perfect matching polytope 206 1666 1680 Perfect numbers 1O08 Perfect set 760 Perfect, H. 438 Perfect, H.A. 522; see “Bryant V.” Perfectly 1-factorable 80 Perfeel graph theorem 267 270 1687 Performance absolute 1633 1634 Performance asymptotic 1633 1634 Performance guarantee 244 246 1547 1634 Performance ratio 1546 1547 Peripheral circuits 58 152 Perko, A. 717; see “Tietavainen A.” Perles, M.A. 438 Perlwitz, M.D. 1990; see “Waterman M.S.” Perm, C. 215; see “Murty K.G.” Permanents 221 1208 2170 Permanents van der Waerdcn’s conjecture 1456 Permutation 1024 1027 1050 Permutation character 631 Permutation digraph 1047 Permutation group 614 1516 1963 2053 2054 Permutation matrix 187 Permutation oligomorphic 1509 Permutation rank 3 1477 Permutation regular 1467 Permutation t-homogeneous 1468 Permutation t-transitive 1468 Permutational isomerization reaction 1965 Permutational isomers 1965 Permutations with distinct cycle length 1127 1171 Permutations with restricted position 1043 Permutations without long increasing subsequences 1155 Perrin, D. 1031; see “Berstel J.” Perron, O. 1140 PERT 2187 Petcrsen, J. 51 89 188 260 Petersen graph 51 54 62—64 75 89 92 189 211 295 296 377 515 548 701 750 752 760 1452 1472 Petersen theorem 188 Petersen, B. 1922 Petersen, K. 1438 1439 Peterson, B.B. 850 Peterson, Ch. 697 Peterson, G.; see Daniels, D. 1997 Peterson, W.W. 806 Petrenjuk, A.Ya. 696 Petrovskil, I.B.. 1761; see “Olemik O.A.” Pfaffian 222 669 1590 1732 1944 Pfafian orientation 223 224 Pfeiffer, F. 162 164; M.” PG 696 Phase transition 358 Phillips, D.T. 125 Phillips, R. 1385 1482 1754 1756—1758; A.” Physical sciences 1958 Pick theorem 947 Pickert, G. 652 Pidgeonhole principle 1334 Piecewise linear 1802 2184; Piepmeyer, L. 839 848; H.” Pierce, T.H. 1969 Piff, M.J. 507 Pinsker, M. 1755 Pinson, E. 1906; see “Cariier J.” Pintz, J.A. 991 Pintz, J.B. 408; see “Ajtai M.” Pintz, J.C. 1350 1438; J.” Pintz, T. 861; see “Komlos J.” Piper, F. 1710 1729; D.” Piper, F.C. 669; see “Hughes D.R” Pippenger, N. 410 425 1755 Pippenger, N.A. 1629; see “Paul W.J.” Piras, F; see “Cerlienco, L” 1131 Pisanski, T. 325 Pittel, B. 369; see “Flajolet P.” Pittel, B.A. 361; see “Janson S.” Pittel, B.B. 360; see “Luczak T.” PL (piecewise linear) 1855 PL (piecewise linear) balls 1855 1859 PL (piecewise linear) map 1860 PL (piecewise linear) sphere 886 1855 1857 1859 PL (piecewise linear) topology 1859 Plambeck, T. 2136 2158; A.” Planar 291 296 494 532 538 540 546 883 1492 1494 Planar 3-colorability 246 Planar dual 55 Planar embedding 55 1557 Planar graph 55 153 237 259 277 306 494 1511 1564 2078 Planar poset 468 Planar space 697 Planar ternary ring 668 Planarity 360 365 493 Plane cubic curve 2180 Plane graph 55 306 Plane of symmetry 884 Plane partition 1057 2174 Plane triangulation 259 260 Planes and hyperpianes 826 Planted plane tree 1140 Plass, M.F. 1888; see “Knuth D.E.” Platonic graphs 5 Platonic solids 897 PlattC.R. 312 Pless symmetry codes 703 Pless, V. 703 727 794 802 806 Plotkin bound 781 Plouffe, S. 1211; see Bergeron F. Plouffe, S.A. 1076; see Sloane N.J.A. Plucker coordinates 2062 Plucker-Grassmann relations 889 Plummer, M.D. 62; see “Holton D.A.” Plummer, M.D.A. 47 66 125 127 147 182—184 190 194—199 206 209 212 216 220 221 223 224 226 263 383 397 1471 1566 1667 2051 2186 2188; L.” Poincare series 2058 2065 Poincare, H. 896 Poinsot, L. 2176 Point graph 684 Point-set duality 501 Pointed polyhedron 877 1655 POINTER 2019 2020 Points-lines-planes conjecture 832 poisson 366 Poisson approximations 1167 Poisson convergent 367 Poisson summation formula 1090 Polansky, O.E. 1974; see “Gutman I.” Polar (dual) polytope 879 Polar body 926 Polar lattice 925 Polar space 663 Polarity 663 671 695 903 Poljak, S. 1555 1584
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