An (r, n)-split coloring of a complete graph is an edge coloring with r colors under which the vertex set is partitionable into r parts so that for each i, part i does not contain K, in color i. This generalizes the notion of split graphs which correspond to (2, 2)-split colorings. The smallest N for which the complete graph Ks has a coloring which is not (r,n)-split is denoted by f,.(n). Balan...

Skoviera, M. and J. ‘&Iii, Regular maps from Cayley graphs, Part i: Balanced Cayley maps, Discrete Mathematics IO9 (1992) 265-276. A Cayley map is a Cayley graph 2-cell embedded in some orientable surface so that the local rotations at every vertex are identical. Two types of Cayley maps are introduced: the balanced and antibalanced Cayley maps. In Part 1, conditions are given uuder which a bal...

Bipartite graphs G = (L, R; E) and H = (L, R; E) are bi-placeabe if there is a bijection f : L ∪ R → L ∪ R such that f(L) = L and f(u)f(v) / ∈ E for every edge uv ∈ E. We prove that if G and H are two bipartite balanced graphs of order |G| = |H | = 2p ≥ 4 such that the sizes of G and H satisfy ‖ G ‖≤ 2p− 3 and ‖ H ‖≤ 2p− 2, and the maximum degree of H is at most 2, then G and H are bi-placeable...

This paper surveys recent results for flag enumeration of polytopes, Bruhat graphs, balanced digraphs, Whitney stratified spaces and quasi-graded posets.