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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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                        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 1798—1801 Lovasz theorem 243 253 267 Lovasz — Simonovits theorem 1238 Lovasz, L. 36 47 64 66 86 94 120 125 127 142 147 149 154 158 166 182—184 190 194—199 201 206 209 211 212 216 220 221 223 224 226 236 240 243 246 249 252 253 263—265 267 269 271 296 383 386—389 396 397 401 402 404 408—411 414-^)16 421 422 424 571 578 579 923 953—955 1238 1275 1297 1319 1385 1415—1417 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 Lovasz’s local lemma 457 1351 1798—1800 Lovasz’s 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 1756—1758 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 1516—1520; 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 MacMahon’s 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. 114 148 149 154—157 159 167 258 333 335 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 Mahler’s 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 Majumdar’s 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 1860—1862 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.” Mann’s 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 1752—1756 Markoff spectrum 934 Markov’s 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 46 384 385 388 395 405 413—416 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 19 185 390 419 483—522 529 649 832 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 492—494 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 486 503 511 529—531 540 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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