Abstract
All (undirected) graphs and digraphs considered are assumed to be finite (if not otherwise stated) and loopless. Multiple edges (arcs) are permitted. For a graph G, let V(G), E(G) and X(G) denote the vertex set, the edge set, and the chromatic number of G, respectively. If X ⊆ V(G) and F ⊆ E(G) then G − X − F denotes the subgraph H of G satisfying V(H) = V(G) − X and E(H) = {xy | xy ∈ E(G) − F and x, y ∉ X}.
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References
N. Alon, The strong chromatic number of a graph, Random Structures and Algorithms 3(1) (1992), 1–7.
N. Alon and M. Tarsi, Colourings and orientations of graphs, Combinatorica 12(2) (1992), 125–134.
D. Z. Du, D. F. Hsu and F. K. Hwang, The Hamiltonian property of consecutived digraphs, Math. Comput. Modelling 17 (1993), no. 11, 61–63.
P. Erdős and N. G. de Bruijn, A colour problem for infinite graphs and a problem in the theory of relations, Nederl. Akad. Wetensch. Proc. Ser. A 54 (=Indag. Math. 13) (1951), 371–373.
P. Erdős, On some of my favourite problems in graph theory and block designs, Le Matematiche, Vol. XLV (1990) Fasc.I, 61–74.
T. Gallai, Kritische Graphen I, Publ. Math. Inst. Hung. Acad. Sci. 8 (1963), 373–395.
M. R. Fellows, Transversals of vertex partitions of graphs, SIAM J. Discrete Math 3 (1990), 206–215.
H. Fleischner, Eulerian Graphs and Related Topics, Part 1, Vol.1, Ann. Discrete Math. 45; Vol. 2, Ann. Discrete Math. 50 (North-Holland, Amsterdam 1990/91).
H. Fleischner and M. Stiebitz, A solution to a colouring problem of P. Erdös, Discrete Math. 101 (1992), 39–48.
H. Sachs, An elementary proof of the cycle-plus-triangles theorem, manuscript.
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© 1997 Springer-Verlag Berlin Heidelberg
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Fleischner, H., Stiebitz, M. (1997). Some Remarks on the Cycle Plus Triangles Problem. In: Graham, R.L., Nešetřil, J. (eds) The Mathematics of Paul Erdös II. Algorithms and Combinatorics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60406-5_13
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DOI: https://doi.org/10.1007/978-3-642-60406-5_13
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