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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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Randell, R.      2069 2070; M.J.
Randic, M.      52 1971 1977
Randic, M.A.      1958; see Klein D.J.
Randic, M.B.      1977; see Trinajstic N.
Random $\mathscr{NP}$      1636
Random $\mathscr{NP}$-completc      1636
Random access machine; see RAM random configurations      1788
Random finite      1463
Random graph      353 1350 1461 1932
Random hypergraph      410
Random infinite      1463
Random node heuristic      1577
Random poset      458
Random r-regular      1462
Random restriction      1804
Random restriction method      2013
Random subproduct      1517
Random tournament      1788
Random variable      365
Random walk      148] 1483 1484 1558 1740 1744
Randomization      1544 2005 2007
Randomized algorithm      1611 1612 1627 1630 1641
Randomized computation      1611
Randomized exchange      1557
Randomized polynomial algorithm      223
Randomized polynomial-time algorithm      1612
Randomized Turing machine      1612 1638
Randrianarimanana, B.      1210; see Louchard G.
Raney, G.      1033
Rank 3 graph      766
Rank axioms      485
Rank function      484486 492 501 521 1844
Rank generating function      512
Rank level      1844
Rank of a flat      497
Rank of a hypergraph      387 414
Rank of a lattice      923
Rank of a matroid      484 490 492
Rank of a permutation group      626 766
Rank of a poset      1843
Rank polynomial      1930 1944
Rank quotient      1547
Rankin, R.A.      1473
Rao, M.R.      1696
Rao, M.R.A.      397; see Conforti M.
Rao, M.R.B.      131 132 207 1658 1662 1667 1680 1681 1696; M.W.
Rao, S.B.      392; see Naik R.N.
Raoult, J.-C.      1194; see Rajolet P.
Rapaport-Strasscr, E.      1472
Raromal, R.A.      1947; see Barahona F.
Rational affine halfspace      1691
Rational polyhedron      1656
Rational solvability      890
Rational vector space      890
Rationality conditions      752 757
Ratliff, H.D.      1882
Ravindra, G.      268; see Parthasaiathy K.R.
Ray method      1210
Ray-Chaudhuri, D.      383 416; C.
Ray-Chaudhuri, D.K.      696 711 1351 1716 1719 2183
Ray-Chaudhuri, D.K.A.      789; see Bose R.C.
Ray-Chaudhuri, D.K.B.      711; see Hanani H.
Raz, R.      2007; see Spieker B.
Razborov, A.A.      2013 2016
Rcgev, A.      1155
Rcndl, F.      199; see Little C.H.C.
Reaction graph      1957 1958
Reaction mechanism      1968 1969
Reaction network      1966 1968
Read, R.C.      236 247 248 2172
Read, R.C; see Polya, G.      1058 1962 2172
Real algebraic numbers      890
Real varieties      1761
Realizable polytope      890
Rec, R.      620
Recession cone      903
Reciprocal lattice      925
Recoloration method      1797
Reconstructible edge      1722
Reconstructible s-edge      1722
Reconstructible strongly      1450 14551457
Reconstructible vertex      1731
Reconstructible weakly      1450
Reconstruction      393 1450 1498 1520
Reconstruction edge      1521
Reconstruction vertex      1520
Recski, A.      522 1913 1919 1921
Rectangular representation of a graph      312
Rectilinear realization      1843
Recurrence      1130 2169
Recursion relations      1961
Redei theorem      28
Redei, L.      28 29 1751 1774 1775
Redfield, J.H.      1960 1962 1965 2172 2177
Redfield-Read superposition theorem      2172
Reduced Euler characteristics      1847
Reduced link diagram      2077
Reduced simplicial homology group      1846
Reducibility      1620
Reducible      2179
Reducible clique      227
Reducible configuration      237
Reduction      1605 1637
Reduction domain      927
Reduction theory      922 926
Reed Muller code      791 1722
Reed Muller rth order binary      792
Reed Solomon code      790
Reed, B.      85 269
Rees, R.      711
Reflection groups      1473
Reflection principle      1152
Reflections      656
Regions in the projective plane      816
Regnier, M.      1192 1194; P.
Regression      474
Regressive      2114
Regular      408 410 412 519
Regular cardinal      2112
Regular cell complex      1860
Regular complex polytopes      1857
Regular graph      7
Regular graph of faithful dimension      843
Regular group      615
Regular hypergraph      415
Regular matroid      505 506 531 536 538 541 543 544 1833
Regular permutation representation      1467
Regular polytope      897
Regular sequence      2058
Regular spread      670
Regular uniform hypergraphs      1471
Regularity lemma      1246 1340
Regularizable      408
Regulus      670
Reid, K.B.      87
Reid, R.      506
Reidemeister moves      2073 2075
Reif, J.      327; see Filote L.S.
Reiman theorem      1240
Reiman, I.      76 1240
Reinelt, G.      1550 1556 1890
Reinelt, G.A.      1572 1573 1696 1950 1951; M.
Reinelt, G.B.      1573; see Juenger M.
Reinelt, O.      1568 1572 1573 1950 1951; F.
Reiner, I.      630; see Curtis C.W.
Reiner, V.      2072; see Edelman P.H.
Reingold, E.M.      1145; see Kapoor S.
Reischuk, R.      2010; see Halstenberg B.
Reisner, G.A.      902 1855 1856
Relative interior      880
Relativized complexity class      1620 1621 1625
Relaxation      1543 1560 1561
Reliability      1932
Remoteness      2145 2149 2150
Renegar, J.      888
Renyi, A.      354 1203
Renyi, A.A.      76 354 355 357 358 361 365 370 373 1241 1242 1461 1463 1482 1486 1508 2179; P.
Repeated angles      845
Repeated block      695
Repeated distances      834
Replaceable net      670
Replication number      695
Replications      2182
Representable matroid      486 503 505 511 529531 540
Representations of symmetric groups      1057
Representative graph      387
Residual design      700
Residually connected geometry      680
Residue of flag      680
Residue theorem      1157
Resistance      1740 1744
Resolution      711
Resolvable design      711
Restricted eigenvalue      750
Restricted linear program      1659
Restricted theorems      1379
Restriction      495 496
Restriction enzymes      1994
Restriction fragments      1993
Restriction of a hypergraph      386
retract      1862
Reuter, K.      455
Reuvers, H.F.H.      717
Reverse lexicograph order      1296
Reversible      2131
reversion      2169
Reverting power series      2170
Revisit      908
Reznick, B.      951
Reznick, B.A.      1145; see Erdos P.
Rice, B.F.      699; see McFarland. R.L.
Rice, S.O.      1140 1141; N.G.
Rices method      1158
Richardson, M.      16
Richert, H.-E.      979 981; H.
Richmond, B.      1194 1202 1203; P.
Richmond, B.A.      1153; see Knopfmacher A.
Richmond, L.B.      60
Richmond, L.B.A.      1116 1191 1212; E.A.
Richmond, L.B.B.      1191; see Gao Z.
Richmond, L.B.C.      1181; see Odlyzko A.M.
Richmond, L.B.D.      1203; see Wright R.A.
Richtcr, R.B.      327; see Fiedler J.R.
Richter, B.      1960; see Ruch E.
Richter, R.B.A.      59; see Gao Z.C.
Richter-Gebert, J.      890
Ricmann-Roch theorem      667
Ridge graph      905
Ridge path      908
Ridges      877 878
Riemann hypothesis      982
Riemann hypothesis for curves      1758
Riemann hypothesis for curves over finite fields      1758
Riemann-Lebesgue lemma      1171
Riemann-Stieltjes integrals      1080
Rigid framework      1915
Rigid-circuit graph      266 267
Rigidity theory      902
Riha, S.      53
Rinaldi, G.      1573; see Jungcr M.
Rinaldi, G.A.      15711573 1881 2188; M.W.
Ringel Youngs theorem      261
Ringel, G.      237 238 261 305 323326 1493 2179
Rinnooy Kan, A.H.G.      1635; see Coflman Jr E.G.
Rinnooy Kan, A.H.G.A.      1635; see Karp R.M.
Rinnooy Kan, A.H.G.B.      1906 1907; B.J.
Rinnooy Kan, A.H.G.C.      20 1545 1882 1906 1907 2188; E.L.
Rinnooy Kan, A.H.G.G.      1878 1882 1888; J.K.
Rinnooy Kan, A.H.G.H.      1545; see Nemhauser G.L.
Riordan, J.      1044 1075 1106 1147 1213 1731
Rival, I      435 1824
Rival, I.      468; see Kelly D.
Rivest Vuillemin theorem      1285
Rivest, R.L.      1285 2027 2030
Rivest, R.L.A.      1550; see Cormen T.H.
Rivest, R.L.B.      1299; see Linial N.
RNA      1990
Robbins, HE.      16 119 148
Roberts, F.S.      1135; see Fishburn P.C.
Roberts, S.      1389; see Grinstead C.
Robertson, N.      8 160 161 166 238 258 304 305 334 336343 391 536 2178
Robertson, N.A.      327; see Fiedler J.R.
Robin son-Schcnsted algorithm      2175
Robinson, G. de B.      633 2175
Robinson, G.C.      252; see Hanson D.
Robinson, R.W.      60 1457
Robinson, R.W.A.      1975; see Canfleld E.R.
Robinson, R.W.B.      1162; see Harary F.
Robinson, R.W.C.      60; see Richmond L.B.
Rock, H.      578; see Fujishige S.
Rockafellar, R.T.      517
Rockmore, D.      1519; see Babai L.
Roddity, Y.      1724.; see Godsil C.D.
Roditty, Y.A.      1522 1523; C.D.
Rodl nibble      1796
Rodl, V.      1351 1357 1557 1765 1766; N.
Rodl, V.A.      1340 1347; V.
Rodl, V.B.      1346; see Duflus D.
Rodl, V.C.      1252 1345 1357 1367; P.
Rodl, V.D.      376 410 411 418 842 860 1248 1307 1310 1321 1341 1371 1372 1381 1383 1393 1796; P.
Rodl, V.E.      459 465; Z.
Rodl, V.F.      1346 1349 1369; R.L.
Rodl, V.G.      1346 1367; H.
Rodl, V.H.      1371; see Matousek J.
Rodl, V.I.      240 424 1333 1337 1340 1351 1356 1369 1370 13731377 13791382 13851389 13911393; J.
Roedl, V.      376 377 714 1306 1333 1346 1347 1349 1351 1366 1374 1375 1377 1380 1386 1387 1442 1796
Rogers, C.A.A.      940; see Coxeter H.S.M.
Rogers, C.A.B      839 842 1310; D.G.
Rogers, CA.      923 936 938940
Rogers, K.      705
Rogers-Ramamijan identity      1038 1942
Roman, S.      2170
Ronan, M.A.      676 679 1822 1857
Roohy-Laleh, E.      1667
Room square      712
Roos, C.      761
Roos, C.A.      675 761; W.H.
Root lattice      767
Root of a tree/arborescence      13 16
Root system      936
Rooted cut      1566
Rooted graph      891
Rooted labeled      1098 1107 1162
Rooted tree      1043 2176
Rooted unlabeled      1070 1195
Rosa, A.      709
Rosa, A.A.      704; see Doyen J.
Rosa, A.B.      703 709; C.C.
Rosa, A.C.      704.; see Mathon R.
Rosa, A.D.      712; see Mendelsohn E.
Rosdle, D.P.      710
Rose, L.L.      2072
Rosenberg, A.G.      1285
Rosenblut, A.      1558; see Metropolis N.
Rosenbluth, M.      1558; see Metropolis N.
Rosenfeld, B.A.      2166; see Ahmedev S.S.
Rosenfeld, M.      910
Rosenfeld, M.A.      89; see Alspach B.
Rosenkrantz, D.J.      1549
Rosenthal, A.S.      1882; see Ratliff H.D.
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