Voir la notice de l'article provenant de la source Library of Science
@article{DMGT_2005_25_3_a11, author = {Frick, Marietjie and van Aardt, Susan and Dlamini, Gcina and Dunbar, Jean and Oellermann, Ortrud}, title = {The directed path partition conjecture}, journal = {Discussiones Mathematicae. Graph Theory}, pages = {331--343}, publisher = {mathdoc}, volume = {25}, number = {3}, year = {2005}, language = {en}, url = {http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a11/} }
TY - JOUR AU - Frick, Marietjie AU - van Aardt, Susan AU - Dlamini, Gcina AU - Dunbar, Jean AU - Oellermann, Ortrud TI - The directed path partition conjecture JO - Discussiones Mathematicae. Graph Theory PY - 2005 SP - 331 EP - 343 VL - 25 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a11/ LA - en ID - DMGT_2005_25_3_a11 ER -
%0 Journal Article %A Frick, Marietjie %A van Aardt, Susan %A Dlamini, Gcina %A Dunbar, Jean %A Oellermann, Ortrud %T The directed path partition conjecture %J Discussiones Mathematicae. Graph Theory %D 2005 %P 331-343 %V 25 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a11/ %G en %F DMGT_2005_25_3_a11
Frick, Marietjie; van Aardt, Susan; Dlamini, Gcina; Dunbar, Jean; Oellermann, Ortrud. The directed path partition conjecture. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 331-343. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a11/
[1] J.A. Bondy, Handbook of Combinatorics, eds. R.L. Graham, M. Grötschel and L. Lovász (The MIT Press, Cambridge, MA, 1995) Vol I, p. 49.
[2] J. Bang-Jensen, Digraphs: Theory, Algorithms and Applications (Springer-Verlag, London, 2002).
[3] C. Berge and P. Duchet, Recent problems and results about kernels in directed graphs, Discrete Math. 86 (1990) 27-31, doi: 10.1016/0012-365X(90)90346-J.
[4] I. Broere, M. Dorfling, J.E. Dunbar and M. Frick, A path(ological) partition problem, Discuss. Math. Graph Theory 18 (1998) 115-125, doi: 10.7151/dmgt.1068.
[5] M. Chudnovsky, N. Robertson, P.D. Seymour and R. Thomas, Progress on Perfect Graphs, Mathematical Programming Ser. B97 (2003) 405-422.
[6] J.E. Dunbar and M. Frick, Path kernels and partitions, JCMCC 31 (1999) 137-149.
[7] J.E. Dunbar and M. Frick, The Path Partition Conjecture is true for claw-free graphs, submitted.
[8] J.E. Dunbar, M. Frick and F. Bullock, Path partitions and maximal Pₙ-free sets, submitted.
[9] M. Frick and F. Bullock, Detour chromatic numbers of graphs, Discuss. Math. Graph Theory 21 (2001) 283-291, doi: 10.7151/dmgt.1150.
[10] M. Frick and I. Schiermeyer, An asymptotic result on the Path Partition Conjecture, submitted.
[11] T. Gallai, On directed paths and circuits, in: P. Erdös and G. Katona, eds., Theory of graphs (Academic press, New York, 1968) 115-118.
[12] F. Harary, R.Z. Norman and D. Cartwright, Structural Models (John Wiley and Sons, 1965).
[13] J.M. Laborde, C. Payan and N.H. Xuong, Independent sets and longest directed paths in digraphs, in: Graphs and other combinatorial topics (Prague,1982) 173-177 (Teubner-Texte Math., 59 1983.)
[14] L.S. Melnikov and I.V. Petrenko, On the path kernel partitions in undirected graphs, Diskretn. Anal. Issled. Oper. Series 1, 9 (2) (2002) 21-35 (Russian).
[15] M. Richardson, Solutions of irreflexive relations, Annals of Math. 58 (1953) 573-590, doi: 10.2307/1969755.
[16] B. Roy, Nombre chromatique et plus longs chemins d'un graphe, RAIRO, Série Rouge, 1 (1967) 127-132.
[17] L.M. Vitaver, Determination of minimal colouring of vertices of a graph by means of Boolean powers of the incidence matrix (Russian). Dokl. Akad. Nauk, SSSR 147 (1962) 758-759.
[18] D.B. West, Introduction to Graph Theory (Prentice-Hall, Inc., London, second edition, 2001).