T. Hoffman, J. Mitchem, and E. Schmeichel, On edge-coloring graphs, Ars Combin., 33 (1992), pp. 119--128. Home/Search Document Not in Database Summary Related Articles Check |
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Chromatic Index Critical Graphs and Multigraphs - Grünewald (2000) (Correct)
....critical multigraph is not # colorable. Another reason to be interested in non elementary critical graph is the computational complexity of finding the chromatic index of a given graph. As shown by Holyer [17] this problem is NP complete. On the other hand, Ho#man, Mitchem, and Schmeichel [16] gave an algorithm which decides in polynomial time, if a graph with maximum degree # contains a subgraph with n vertices and at least #n 2## 1 edges. Hence, the chromatic index of a graph G with fixed maximum degree # can be determined in polynomial time, if we know that G does not contain a ....
....the following conjecture by Seymour. Conjecture 5.1 ( 26] There is no planar non elementary critical graph. A proof of Seymour s conjecture would imply not only the four color theorem, but also the existence of a polynomial algorithm determining the chromatic index for any planar graph (see [16]) One more consequence would be that every planar graph with maximum degree at lest 6 is in class one. This weaker conjecture known as the planar graph conjecture was formulated by Vizing [31] in 1965 who also proved the case #(G) # 8. Hence, the two cases # = 6 and # = 7 remain open. In this ....
T. Hoffman, J. Mitchem, E. Schmeichel, On edge-coloring graphs, Ars Combin. 33 (1992), 119--128
The Four Colour Theorem as a possible corollary of binomial.. - Matiyasevich (1998) (5 citations) (Correct)
....way of proving the Four Colour Theorem by taking advantage of recent progress in finding closed forms for binomial summations. 1 Introduction The famous Four Color Conjecture (4CC) has, as many other great problems have, numerous equivalent reformulations (see, for example, 4] 5] [6], 7] 8] 9] 10] 11] 13] 18] and further references in these papers) Now that we have the remarkable work of K. Appel, W. Haken and J. Koch [1, 2, 3] these reformulation can be viewed as corollaries of the Four Colour Theorem (4CT) Nevertheless, still there is some interest in such ....
Todd Hoffman, John Mitchem, Edward Schmeichel. On edge-coloring graphs. Ars Combinatoria 33 (1992), 119--128.
One Probabilistic Equivalent of the Four Color Conjecture - Matiyasevich (2003) (Correct)
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T. Hoffman, J. Mitchem, and E. Schmeichel, On edge-coloring graphs, Ars Combin., 33 (1992), pp. 119--128.
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