## Proceedings of the Southeastern Conference on Combinatorics, Graph Theory, and Computing, Volume 4 |

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Page 126

vertex of degree lesS than five and thus a

Suppose e = (u^,u2) is an edge in a triangulation G and Uj/U^ are the two

vertices incident with triangles incident with e. The graph G - (u^,u2) + (u^u.) is

denoted by ...

vertex of degree lesS than five and thus a

**four coloring**of the new graph.Suppose e = (u^,u2) is an edge in a triangulation G and Uj/U^ are the two

vertices incident with triangles incident with e. The graph G - (u^,u2) + (u^u.) is

denoted by ...

Page 127

u2 FIGURE 1 Similarly in a

assigned to at least one vertex from V^,...,^. If not G can be four colored. Pick a

this ...

u2 FIGURE 1 Similarly in a

**four coloring**of Gj the colors C and D must beassigned to at least one vertex from V^,...,^. If not G can be four colored. Pick a

**four coloring**of G2 in which Uj is colored A and and u^+1 are colored B. Transferthis ...

Page 128

Since G is irreducible 9e^(G) is four colorable. Fix a

assume u^ and u4 are colored A and u^ is colored B. If U2 and Ug are not

assigned the same color we have a

assume U2 ...

Since G is irreducible 9e^(G) is four colorable. Fix a

**four coloring**of 6e^(G) andassume u^ and u4 are colored A and u^ is colored B. If U2 and Ug are not

assigned the same color we have a

**four coloring**of 9e^(9e (G)); hence weassume U2 ...

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2-colorable 4TH S-E CONF abelian group adjacent algorithm array of order balanced incomplete block Baumert-Hall array bicritical binary bipartite graph block design boundary colorations braid chain-group circuit Combinatorial Theory conjecture consider construction contains core cycle defined definition denote digits edges equation example exist finite four coloring given graph G Graph Theory Hadamard matrices hamiltonian Hamiltonian graphs hence hypergraph incidence geometry incidence matrix incomplete block design integer isomorphic Jennifer Seberry k-tuples labeled Lemma Let G lower bound Math matroid maximal snakes minimal n-set nodes obtained occurs pair parameters partially ordered partially ordered set partition perfect 1-factorization permutation groups planar graph polynomial prime power problem PROC projective plane Proof reduced sequences Room square satisfy skew Stanton starter subcube subset Suppose symmetric snake T-sequence Table tactical configurations Theorem tree Turyn upper bound values vertices wreath