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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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Locally planar graph      262
Locally polar space      683
Location problem      398
Locbl, M.      1355 1356
Locke, S.C.      38 39
Locke, S.C.A.      37 38; J.A.
Locke, S.C.B.      36; see Egawa Y.
Loebl, M.      1340 1347; P.
Lofgren, L.      594
Log-concavity      1110 1477
Log-cost RAM      1608
Logan, B.F.      1155
Logarithmic 1-forms      2071
Logarithmic density      994
Logarithmic differential forms      2070
Logarithmic space      1637 1638
Logarithmic vector fields      2070
Lollipop      20
Lollipop lemma      20
Lomonosov, M.V.A.      149 150; E.A.
Lomonosov, M.V.B.      163 167
Lomonosov, M.V.C.      167; see Karzanov A.V.
Lomonosov, M.V.D.      62; see Kelmans A.K.
Lone, Z.      84; see Kouider M.
Longest cycle      372
Longest cycle in a random permutation      1167
Longest path      2187
Loop      5 416 490 492 493 498 512
Loop (in a hypergraph)      386
Loopy game      2121
Lorea, M.      407
Lorea, M.A.      423; see Hansen P.
Lottery number      715
Louchard, G.      1210
Lovasz replacement theorem      267
Lovasz sieve      17981801
Lovasz theorem      243 253 267
Lovasz Simonovits theorem      1238
Lovasz, L.      36 47 64 66 86 94 120 125 127 142 147 149 154 158 166 182184 190 194199 201 206 209 211 212 216 220 221 223 224 226 236 240 243 246 249 252 253 263265 267 269 271 296 383 386389 396 397 401 402 404 408411 414-^)16 421 422 424 571 578 579 923 953955 1238 1275 1297 1319 1385 14151417 1449 1455 1456 1464 1466 1470 1471 1473 1497 1498 1521 1548 1558 1559 1566 1588 1590 1593 1654 1667 1672 1687 1689 1695 1712 1713 1719 1720 1723 1724 1732 1736 1740 1774 1775 1825 1827 1830 1832 1833 1862 1920 1921 1944 2005 2009 2011 2051 2186 2188
Lovasz, L.A.      1741; see Aleliunas B.
Lovasz, L.B      1638.; see Aletiunas R.
Lovasz, L.C.      423 1827; N.
Lovasz, L.D.      1499 1501; L.
Lovasz, L.E.      865 903 1828; I.
Lovasz, L.F.      36; see Bermond J.-C.
Lovasz, L.G.      1762 1831 1833 1850 1857; A.
Lovasz, L.H.      36 158; J.A.
Lovasz, L.I.      1673; see Cook W.
Lovasz, L.J.      507; see Dress A.
Lovasz, L.K.      210 1838; J.
Lovasz, L.L.      422 425 456 837 840 865 1313 1319 1351 1798; P.
Lovasz, L.M.      546; see Gerards B.
Lovasz, L.N.      253; see Greenwell D.
Lovasz, L.O.      1464; see Greenwell D.L.
Lovasz, L.P.      236 265 267 269 271 569 1545 1570 1592 1654 1662 1663 1689 1694 1695 1736 1920 2016 2042; M.
Lovasz, L.R.      1566; see Hurkens C.A.J.
Lovasz, L.S.      941; see Kannan R.
Lovasz, L.T.      521 522 582 583 1546 1830; B.
Lovasz, L.U.      953 954 1663; A.K.
Lovasz, L.V.      1557 1590; N.
Lovasz-reduced      953
Lovasz;s lattice basis reduction algorithm      953
Lovaszs local lemma      457 1351 17981800
Lovaszs perfect graph theorem      1689
Low vertex      255
Lower asymptotic density      935 982
Lower rank      1547
Lower record      1025
Lower-bound theorem      902 905
Lowner-John ellipsoid      2042
Loyd, S.      2137
lp      see Linear programming
LP-solver      1574
LSG      see Latin square graph
lth shadow      1295
Lu, J.-X.      710
Lubachevsky, B.D.      1146; see Greenberg A.G.
Lubell, D.      1270 2186
Lubiw, A.      399 400 1518
Lubotzky, A.      1385 1482 1754 17561758
Lubotzky, A.A.      1484 1485; L.
Luby, M.      1442
Luby, M.A.      1555; see Haken A.
Lucas, E.      88 2170 2176
Lucasta      2150
Lucchesi, CL.      120 1676
Luczak, T.      355 360 361 373 375 376
Luczak, T.A.      361 363; S.
Lueker, G.S.      1131
Lueker, G.S.A.      1635; see Coflman Jr.E.G.
Lueker, G.S.B.      1574; see de la Vega Fernandez
Luks equivalence class      1514
Luks, E.M.      1511 1512 1515 1516
Luks, E.M.A.      1449 1511 1512 1514 15161520; L.
Luks, E.M.B      1517.; see Furst M.L.
Lunardon, G.      661; see Bader L.
Lund, C.      246 247
Lund-Yannakakis theorem      246
Lundell, A.T.      1848 1859 1861
Luneburg, H.      661
Lunelli, L.      658
Lunn, A.C.      2172 2177
Lutton, J.L.      1997; see Bonomi E.
Lyndon, R.C.      1494
Lyons, R.      1504; see Gorenstein D.
m-separation      584
Maamoun, M.      83
Maass, W.      1713 2005 2011; A.
Macaulay, F.S.      896
Macbeath, A.M.      1488
MacDonald, I.G.      948
MacGillivray, G.      276; see Bang-Jensen J.
Machine scheduling      1578
Machine-scheduling problem      1633
MacLane, S.      55 308
Maclunes, C.R.      704 2183
MacMahon, RA.      2171 2173 2174
MacMahons master theorem      2171
MacNeish, H.F.      705 2182
Macpherson, H.D.      629 1505
Macpherson, H.D.A.      640; see Adeleke S.A.
Macpherson, H.D.B.      627 1507 1510; W.M.
Macpherson, H.D.C.      640 641; R.
Macsyma      1210
MacWilliams theorem      779
MacWilliams transform      780
MacWilliams, F.J.      673 703 715 721 750 763 765 776 779 780 793 794 796 801 802 806 1722 2183
MacWilliams, F.J.A.      727 763 765; M.R.
MacWilliams, J.      716
Mader, W.      114 148 149 154157 159 167 258 333 335 1469
Madras, N.      1940
Maggiora, G.M.      1958 1977; M.A.
Magic squares      2165 2180
Magidor, M.      2104; see Foreman M.D.
Magliveras, S.S.      2184
Magliveras, S.S.A.      703; see Kramer E.S.
Magliveras, S.S.B.      702 703; D.W.
Magnanli, T.L.      114 125 128; R.K.
Magnus, W.      1494 1751
Maheshwari, S.N.      128 143; J.
Maheswari, S.N.      128; see Malhotra V.M.
Mahjoub, A.R.      1568 1570 1696 2048; F.
Mahler, K.      926 931 1206
Mahlers selection theorem      931
Mahlo cardinals      2098
Mahlo, p.      2098
Mahmoud, H.S.      1204 1205 1210 1213
Maier, H.      981
Maier, H.A.      991; see Erdos P.
Maikov chains      1558 1740
Maillct, E.      625
Main, R.A.      507 508; A.W.
Majindar, K.N.      700 1708
Majority function      2013 2014
Majumdar, K.N.      700
Majumdars inequality      700
Makai, E.      831
Makai, E.A.      836; see Erdos P.
Makespan      1578
Malgrange, B.      1137
Malhotra, VM.      128
Malitz, S.M.      317
Mallion, R.B.      1972
Mallows, C.L.      1108
Malyshev, V.A.      1208
Manalastas, Jr.P.      45; see Chen C.C.
Manber, R.      223; see Klee V.
Mandel, A.      887 1836 1837 1857 18601862
Mandel, A.A.      1837 1838; J.
Mani, P.      884 886 908 1459
Mani, P.A.      907; see Blind R.
Mani, P.B.      1857; see Bruggesser H.
Mani, P.C.      887 901; M.
Mani, P.D.      158 166; D.G.
Mani-Levitska, P.      311
Manifold      880
Manin, Y.A.      667
Mann theorem      984 985
Mann, H.B.      699 700
Mann, H.B.A      716.; see MacWilliams J.
Manns inequality      700
Manoussakis, Y.      69; see Haggkvist R.
Manoussakis, Y.A.      68; see Bang-Jensen J.
Mansfield, A.      317
Mansour, Y.      1299; see Linial N.
Mantel, W      12 1234
Manvel, B.      245
Manvel, B.A.      910; see Holton D.A.
MAP      1487 1488 1493
Map covering      1454
Map distance      1994
Maple      1210
Maps of DNA      1993
Mar, A.      862; see Katchalski M.
Marble, G.; see Matula, D.W.      245
Marcus, M.      755
Margulis graph      1265
Margulis, G.A.      958 1265 1385 1482 17521756
Markoff spectrum      934
Markovs inequality      356 1811
Markvorsen, S.      1484
Marriage theorem      185 2041 2052 2185
Mars, M.      1297
Marsh III, A.B.      209 1679; W.H.
Martel, C.      573 576 577; E.L.
Martello, S.      1903; see Fischetti M.
Martens, H.      958
Martin, A.      1571 1573; M.
Martin-Lof, A.      168; see Kleitman D.J.
Martingale      373
Martini, H.      831; see Makai E.
Maruani, J.      1965
Maruoka, A.      1755 1756; Sh.
Marusic, D.      1468 1473 1474
Masavctas, K.A.      1968
Maschke theorem      630
Maschke, H.      1491
Mason, D.W.      87; see Alspach B.
Mason, J.      510
Mason, J.H.      832
Matching      181 388 412 500 1044 1316 1690 1973 2051
Matching algorithm      191 1589
Matching covered graph      195
Matching graph bicritical      1470
Matching graph matching critical      1470
Matching lattice      210
Matching matroids      500
Matching number      46 384 385 388 395 405 413416 1295
Matching polyhedron      206
Matching polynomial      1731 1941 1973 1976
Matching polytope      208 412 1651 1665 1679 1692
Matching problem      922 1547 1578
Matchstick geometries      516
Mate, A.      1336 1389 2093; P.
Mathematica      1210
Mathematical induction      2166
Mather, J.      1849 1851
Mathieu groups      622 625 716 2183
Mathieu, E.      627
Mathon, R.      704 1514
Mathon, R.A.      753
Matousek, J.      1371 1425 1437
Matousek, J.A      1357.; see Larmann D.
Matousek, J.B.      1355; see Loebl M.
Matrix circulant      1495
Matrix negative type      2047
Matrix representation      630
Matrix tree theorem      1047
Matroid      19 185 390 419 483522 529 649 832 1545 1546 1587 1830 1857 2065 2066 2077 2178
Matroid algebraic      486 507
Matroid algorithm      556
Matroid base of      484 492 493 502 512 1307
Matroid binary      506 519 529 530 536 538 548
Matroid bond      493
Matroid cocycle      493 494 515
Matroid cographic      493 494 505
Matroid connected      491 493 504 584
Matroid deleting of elements of      494 495
Matroid dependent set of      483 488 495
Matroid direct sum      651
Matroid disconnected      491
Matroid dual      492494
Matroid duality      492
Matroid Fano      488 503 514
Matroid flat of      484 490 497
Matroid free      486 494 497 504
Matroid graphic      491 494 505 516 518 532 547 594
Matroid induced      500
Matroid intersection      558
Matroid intersection algorithm (MIA)      559
Matroid intersection polytope theorem      564
Matroid intersection theorem      503 558
Matroid matching      500
Matroid modular      504
Matroid non-Fano      507
Matroid non-Pappus      504 508
Matroid non-representable      504
Matroid non-separable      491
Matroid orientable      1835
Matroid oriented      517 519 604 887 888 1834 1835 2066
Matroid parallel elements of      490 498
Matroid partition theorem      502 561
Matroid partitioning      561
Matroid paving      499
Matroid polygon      486 488
Matroid rank of      484 490 492
Matroid regular      505 506 531 536 538 541 543 544 1833
Matroid representable      486 503 511 529531 540
Matroid simple      490 498 830
Matroid theory      496
Matroid transversal      500 501 506 508
Matroid underlying      1835
Matroid uniform      486 489 491 494 497
Matroid Vamos      659
Matroid vectorial      486
Matroid, algebraic over a field      507
Matsumoto, M.      1297
Matsumoto, M.A.      1297; see Frankl P.
Mattheiss, T.H.      881
Matthews, M.      62 66
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