CID 2003 Abstracts - Colourings, Independence and Domination

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50 abstracts TREES WITH NUMEROUS EXTREMAL SUBFORESTS Zdzis̷law Skupień AGH University of Science and Technology, Kraków, Poland A review of results, old and new, on the structure of n-vertex trees with maximal numbers of some selected extremal subforests will be presented. These subforests are some factors (e.g., maximum linear forests), maximal matchings, maximal independent sets, or kernels with various distance bounds. Keywords: tree, independent set, kernel, maximizing cardinality, structure. AMS Subject Classification: 05C05, 05C69, 05C35, 05C75, 05A16, 39A10. References [1] D. Bród, Z. Skupień, Trees with many (3, 1)-kernels, to appear. [2] Joanna Górska, Z. Skupień, Trees with maximum number of maximal matchings, to appear. [3] J.W. Moon, L. Moser, On cliques in graphs, Israel J. Math. 3(1) (1965) 23–28. [4] Z. Skupień, Path partitions of vertices and hamiltonity of graphs, in: M. Fiedler, ed., Recent Advances in Graph Theory (Proc. Symp. Prague 1974), Akademia, Praha (1975) 481–491. [5] Z. Skupień, On counting maximum path-factors of a tree, in: Algebra und Graphentheorie (Proc. Siebenlehn 1985 Conf.), Bergakademie Freiberg, Sektion Math. (1986) 91–94. [6] Z. Skupień, From tree path-factors and doubly exponential sequences to a binomial inequality, in: R. Bodendiek and R. Henn, eds., Topics in Combinatorics and Graph Theory (Essays in Honour of Gerhard Ringel), Physica-Verlag, Heidelberg (1990) 595–603. [7] I. Tomescu, Le nombre maximum de cliques et de recouvrements par cliques des hypergraphes chromatiques complets, Discrete Math. 37 (1981) 263–271. [8] H.S. Wilf, The number of maximal independent sets in a tree, SIAM J. Alg. Discrete Math. 7 (1986) 125–130. [9] J. Zito, The structure and maximum number of maximum independent sets in trees, J. Graph Theory 15(2) (1991) 207–221.
abstracts 51 ON SELF-COMPLEMENTARY SUPERGRAPHS OF (N, N)-GRAPHS A. Pawe̷l Wojda, Mariusz Woźniak and Irmina A. Zio̷lo AGH University of Science and Technology, Kraków, Poland We consider simple graphs without loops and multiple edges. An embedding of a graph G is a permutation σ on V (G) such that if an edge xy belongs to E(G) then σ(x)σ(y) does not belong to E(G). If there exists an embedding of G we say that G is embeddable. A graph G of order n ≡ 0, 1 (mod 4) is self-complementary if it is isomorphic to its complement. A graph G of order n ≡ 2, 3 (mod 4) is almost selfcomplementary if G is of size 1 2 (( n 2) −1) and G is a subgraph of its complement. It is evident that subgraphs of self-complementary graphs are embeddable. In general the converse is not true. It is proved that every embeddable graph of order n and size at most n − 1 is a subgraph of self-complementary or almost self-complementary, respectively, graph of order n ([1] cases n ≡ 0, 1 (mod 4), [2] cases n ≡ 2, 3 (mod 4)). We prove that, with one exception, for each embeddable graph of order n and size n there exists a self-complementary or an almost self-complementary, respectively, supergraph of order n. Keywords: packing of graphs, self-complementary graph. AMS Subject Classification: 05C70. References [1] A. Benhocine, A.P. Wojda, On self-complementation, J. Graph Theory 8 (1985) 335–341. [2] M. Woźniak, Embedding graphs of small size, Discrete App. Math. 51 (1994) 233–241.
Page 1 and 2: 10th WORKSHOP 0N GRAPH THEORY COLOU
Page 3 and 4: 4 contents H. Furmańczyk Equitable
Page 5 and 6: program 7 PRELIMINARY PROGRAM 13.45
Page 7 and 8: program 9 Chair: A. Pawe̷l Wojda 1
Page 9 and 10: program 11 Chair: Douglas F. Rall 1
Page 11 and 12: abstracts 13 AN ALGORITHM FOR GENER
Page 13 and 14: abstracts 15 GENERATING LABELED CUB
Page 15 and 16: abstracts 17 GAME LIST COLOURING OF
Page 17 and 18: abstracts 19 PARTITION PROBLEMS OF
Page 19 and 20: abstracts 21 ADDITIVE HEREDITARY PR
Page 21 and 22: abstracts 23 HAMILTONIAN PATH SATUR
Page 23 and 24: abstracts 25 THE UNIQUELY ONE-ONE R
Page 25 and 26: abstracts 27 INDUCED RAMSEY CLASSES
Page 27 and 28: abstracts 29 SIERPIŃSKI GRAPHS: L(
Page 29 and 30: abstracts 31 HAPPY COLORINGS OF HYP
Page 31 and 32: abstracts 33 ON COMPLETE TRIPARTITE
Page 33 and 34: abstracts 35 COMBINATORIAL LEMMAS F
Page 35 and 36: abstracts 37 COMPETITIVE GRAPH COLO
Page 37 and 38: abstracts 39 ON (k, l)-KERNEL PERFE
Page 39 and 40: abstracts 41 EXTENDABILITY AND NEAR
Page 41 and 42: abstracts 43 DOMINATING BIPARTITE S
Page 43 and 44: abstracts 45 Example 2. The propert
Page 45 and 46: abstracts 47 DOMINATION AND INDEPEN
Page 47: abstracts 49 ON GENERALIZED k-DEGEN
Page 51 and 52: participants 53 LIST OF PARTICIPANT
Page 53 and 54: late abstracts 55 A COMPLETE PROOF

CID 2003 Abstracts - Colourings, Independence and Domination

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