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4.022  Articles
1 of 403 pages  |  10  records  |  more records»
Let k = 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from Zk and that induces a proper vertex colori... see more

A proper edge coloring of a class 2 graph G is minimal if it contains a color class of cardinality equal to the resistance r(G) of G, which is the minimum number of edges that have to be removed from G to obtain a graph which is ?(G)-edge colorable, ... see more

We consider the question of when a triangulation with a Grünbaum coloring can be edge-colored with three colors such that the non-facial 3-cycles also receive all three colors; we will call this a strong Grünbaum coloring. It turns out that for the s... see more

We develop a connection between DP-colorings of kk-uniform hypergraphs of order nn and coverings of nn-dimensional Boolean hypercube by pairs of antipodal (n-k)(n-k)-dimensional faces. Bernshteyn and Kostochka established a lower bound on the number of ed... see more

Given a partial edge coloring of a complete graph KnK_n and lists of allowed colors for the non-colored edges of KnK_n, can we extend the partial edge coloring to a proper edge coloring of KnK_n using only colors from the lists? We prove that this questio... see more

Let G be a connected plane graph with vertex set V and edge set E. For X ? {V, E, V ? E}, two elements of X are facially adjacent in G if they are incident elements, adjacent vertices, or facially adjacent edges (edges that are consecutive ... see more

Consider the collection of edge bicolorings of a graph that are cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and reversing colo... see more


Motivated by a 40-year-old problem due to Peter Cameron on extending partial parallelisms, we provide necessary and sufficient conditions under which one can extend an rr-factorization of a complete 33-uniform hypergraph on mm vertices, K3mK_m^3, to an ss... see more

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