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Graham R.L., Grotschel M., Lovasz L. Handbook of combinatorics (vol. 1)
Graham R.L., Grotschel M., Lovasz L.  Handbook of combinatorics (vol. 1)









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: Handbook of combinatorics (vol. 1)

: Graham R.L., Grotschel M., Lovasz L.

:

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.
The 20 articles in Volume 1 deal with structures while the 24 articles in Volume 2 focus on aspects, tools, applications, and horizons.


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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
OBrien, E.A.      1484; see Celler F.
OBrien, R.C.      87
OKeefe, E.S.      709
ONan, M.E.      631
ONan-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 15711573 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
Pascals 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 265267 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 Waerdcns 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 6264 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 17561758; 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 182184 190 194199 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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