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2013 | 33 | 1 | 147-165
Tytuł artykułu

On Maximum Weight of a Bipartite Graph of Given Order and Size

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The weight of an edge xy of a graph is defined to be the sum of degrees of the vertices x and y. The weight of a graph G is the minimum of weights of edges of G. More than twenty years ago Erd˝os was interested in finding the maximum weight of a graph with n vertices and m edges. This paper presents a complete solution of a modification of the above problem in which a graph is required to be bipartite. It is shown that there is a function w*(n,m) such that the optimum weight is either w*(n,m) or w*(n,m) + 1.
Wydawca
Rocznik
Tom
33
Numer
1
Strony
147-165
Opis fizyczny
Daty
wydano
2013-03-01
online
2013-04-13
Twórcy
  • Institute of Mathematics P.J. Šafárik University Jesenná 5, 04001 Košice, Slovakia, mirko.hornak@upjs.sk
Bibliografia
  • [1] O.V. Borodin, Computing light edges in planar graphs, in: Topics in Combinatorics and Graph Theory, R. Bodendiek and R. Henn (Ed(s)), (Physica-Verlag, Heidelberg, 1990) 137-144.
  • [2] H. Enomoto and K. Ota, Connected subgraphs with small degree sum in 3-connected planar graphs, J. Graph Theory 30 (1999) 191-203. doi:10.1002/(SICI)1097-0118(199903)30:3h191::AID-JGT4i3.0.CO;2-X[Crossref]
  • [3] I. Fabrici and S. Jendrol’, Subgraphs with restricted degrees of their vertices in planar 3-connected graphs, Graphs Combin. 13 (1997) 245-250.
  • [4] B. Grünbaum, Acyclic colorings of planar graphs, Israel J. Math. 14 (1973) 390-408. doi:10.1007/BF02764716[Crossref]
  • [5] J. Ivančo, The weight of a graph, in: Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity, J. Neˇsetˇril and M. Fiedler (Ed(s)), (North- Holland, Amsterdam, 1992) 113-116.
  • [6] J. Ivančo and S. Jendrol’, On extremal problems concerning weights of edges of graphs, in: Sets, Graphs and Numbers, G. Hal´asz, L. Lov´asz, D. Mikl´os and T. Sz˝onyi (Ed(s)), (North-Holland, Amsterdam, 1992) 399-410.
  • [7] E. Jucovič, Strengthening of a theorem about 3-polytopes, Geom. Dedicata 13 (1974) 233-237. doi:10.1007/BF00183214
  • [8] S. Jendrol’ and I. Schiermeyer, On a max-min problem concerning weights of edges, Combinatorica 21 (2001) 351-359. doi:10.1007/s004930100001[Crossref]
  • [9] S. Jendrol’, M. Tuhársky and H.-J. Voss, A Kotzig type theorem for large maps on surfaces, Tatra Mt. Math. Publ. 27 (2003) 153-162.
  • [10] A. Kotzig, Contribution to the theory of Eulerian polyhedra, Mat.-Fyz. ˇ Casopis. Slovensk. Akad. Vied 5 (1955) 111-113.
  • [11] J. Zaks, Extending Kotzig’s theorem, Israel J. Math. 45 (1983) 281-296. doi:10.1007/BF02804013[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1674
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