1934
DOI: 10.1002/sapm1934131363
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A Six Color Problem

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Cited by 71 publications
(53 citation statements)
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“…Heawood Although the Klein bottle has characteristic 0, Franklin (1934) proved that it is only 6-chromatic, and found the following &chromatic map on the Klein bottle: It has been shown that, with the sole exception of the Klein bottle, equality holds in (111.2) for every surface S of characteristic n C2. This result is known as the map colour theorem (see Ringel, 1974 …”
Section: The Platonic Graphsmentioning
confidence: 99%
“…Heawood Although the Klein bottle has characteristic 0, Franklin (1934) proved that it is only 6-chromatic, and found the following &chromatic map on the Klein bottle: It has been shown that, with the sole exception of the Klein bottle, equality holds in (111.2) for every surface S of characteristic n C2. This result is known as the map colour theorem (see Ringel, 1974 …”
Section: The Platonic Graphsmentioning
confidence: 99%
“…Thus, as is well known, ju(2-sphere) = 4, «(projective plane) = 6, jtt(torus) = 7 and jn(Klein's bottle) = 8 (see [5]). The following lemma is obvious:…”
Section: Corollarymentioning
confidence: 71%
“…G(ty) contains the subgroups G" G2, G3 where, in addition to the identity, G, contains the permutations (1, 3)(5, 7), (1, 7)(3, 5) and (1,5) (3, 7); G2 contains (2, 6)(4, 8), (2,8)(4, 6) and (2, 4) (6,8); and G3 contains (1, 2)(3, 4)(5, 6)(7, 8). G, and G2 are Klein groups.…”
Section: -37 46 -35 68 -57mentioning
confidence: 99%
“…Anyway, these experimental results are in agreement with graph col-oring theory. As a matter of fact, that theory also states that at most 6 colors are required to color any map on the plane or the sphere [8]. Of course, and as repeatedly mentioned in the paper, the Four Color Theorem [17] demonstrates that the necessary number of colors is 4.…”
Section: Theory and Parameters In Practicementioning
confidence: 87%