Geodesic
Magic and supermagic dense bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 583-591.

Voir la notice de l'article provenant de la source Library of Science

A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.
Keywords: magic graphs, supermagic graphs, bipartite graphs 
@article{DMGT_2007_27_3_a15,
     author = {Ivanco, Jaroslav},
     title = {Magic and supermagic dense bipartite graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {583--591},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a15/}
}
TY  - JOUR
AU  - Ivanco, Jaroslav
TI  - Magic and supermagic dense bipartite graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 583
EP  - 591
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a15/
LA  - en
ID  - DMGT_2007_27_3_a15
ER  - 
%0 Journal Article
%A Ivanco, Jaroslav
%T Magic and supermagic dense bipartite graphs
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 583-591
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a15/
%G en
%F DMGT_2007_27_3_a15
Ivanco, Jaroslav. Magic and supermagic dense bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 583-591. http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a15/

[1] A. Czygrinow and H.A. Kierstead, 2-factors in dense bipartite graphs, Discrete Math. 257 (2002) 357-369, doi: 10.1016/S0012-365X(02)00435-1.

[2] M. Doob, Characterizations of regular magic graphs, J. Combin. Theory (B) 25 (1978) 94-104, doi: 10.1016/S0095-8956(78)80013-6.

[3] J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Combinatorics #DS6 36 (2003).

[4] N. Hartsfield and G. Ringel, Pearls in Graph Theory (Academic Press, Inc., San Diego, 1990).

[5] J. Ivanco, On supermagic regular graphs, Mathematica Bohemica 125 (2000) 99-114.

[6] J. Ivanco, Z. Lastivková and A. Semanicová, On magic and supermagic line graphs, Mathematica Bohemica 129 (2004) 33-42.

[7] R.H. Jeurissen, Magic graphs, a characterization, Europ. J. Combin. 9 (1988) 363-368.

[8] S. Jezný and M. Trenkler, Characterization of magic graphs, Czechoslovak Math. J. 33 (1983) 435-438.

[9] J. Moon and L. Moser, On Hamiltonian bipartite graphs, Isr. J. Math. 1 (1963) 163-165, doi: 10.1007/BF02759704.

[10] J. Sedlácek, On magic graphs, Math. Slovaca 26 (1976) 329-335.

[11] J. Sedlácek, Problem 27, in: Theory of Graphs and Its Applications, Proc. Symp. Smolenice (Praha, 1963) 163-164.

[12] B.M. Stewart, Magic graphs, Canad. J. Math. 18 (1966) 1031-1059, doi: 10.4153/CJM-1966-104-7.

[13] B.M. Stewart, Supermagic complete graphs, Canad. J. Math. 19 (1967) 427-438, doi: 10.4153/CJM-1967-035-9.