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- Dan Archdeacon
- Journal of Graph Theory
- 1981

- Dan Archdeacon, Joan Hutchinson, Atsuhiro Nakamoto, Seiya Negami, Katsuhiro Ota
- Journal of Graph Theory
- 2001

It has been shown that every quadrangulation on any nonspherical orientable closed surface with a sufÂ®ciently large representativity has chromatic number at most 3. In this paper, we show that a quadrangulation G on a nonorientable closed surface Nk has chromatic number at least 4 if G has a cycle of odd length which cuts open Nk into an orientable surface.â€¦ (More)

- Dan Archdeacon
- Journal of Graph Theory
- 1987

- Dan Archdeacon
- Journal of Graph Theory
- 1984

'The 4-Color Theorem (4CT) states that for any connected, bridgeless graph embedded in the plane, one can properly 4-color the faces, i.e., assign one of 4 colors to each face (region) such that two faces which meet along a common edge receive distinct colors. Closely related to the 4CT is the concept of Tait colorings of a cubic graph, i.e., a 3coloring ofâ€¦ (More)

- Dan Archdeacon, Phil Huneke
- J. Comb. Theory, Ser. B
- 1989

- Dan Archdeacon
- J. Comb. Theory, Ser. B
- 1992

- Dan Archdeacon
- Discrete Mathematics
- 1992

- Dan Archdeacon, Charles J. Colbourn, Isidoro Gitler, J. Scott Provan
- Journal of Graph Theory
- 2000

A graph is Y Y-reducible if it can be reduced to a vertex by a sequence of series-parallel reductions and Y Y-transformations. Terminals are distinguished vertices which cannot be deleted by reductions and transformations. In this paper we show that four-terminal planar graphs are Y Y-reducible when at least three of the vertices lie on the same face. Usingâ€¦ (More)

- Dan Archdeacon, R. Bruce Richter, Jozef SirÃ¡n, Martin Skoviera
- Australasian J. Combinatorics
- 1994

In this article we generalize both ordinary and permutation voltage constructions to obtain all branched coverings of maps. We approach a map as a set of flags together with three fixed-point-free involutions and relate this approach with other standard representations. We define a lift as a function from these flags into a group. Ordinary voltage andâ€¦ (More)

- Dan Archdeacon, C. Paul Bonnington, Charles H. C. Little
- Journal of Graph Theory
- 1995

A cycle in a graph is a set of edges that covers each vertex an even number of times. A cocycle is a collection of edges that intersects each cycle in an even number of edges. A bicycle is a collection of edges that is both a cycle and a cocycle. The cycles, cocycles, and bicycles each form a vector space over the integers modulo two when addition isâ€¦ (More)