In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) — the irregular coloring number, and hence verify the conjecture when G is a vertexdisjoint union of paths. We also investigate the point-dist...

Given a graphG = (V,E), a (d, k)-coloring is a function from the vertices V to colors {1, 2, . . . , k} such that any two vertices within distance d of each other are assigned different colors. We determine the complexity of the (d, k)-coloring problem for all d and k, and enumerate some interesting properties of (d, k)-colorable graphs. Our main result is the discovery of a dichotomy between p...

In an edge-colored graph (G,c), let dc(v) denote the number of colors on edges incident with a vertex v G and δc(G) minimum value over all vertices v∈V(G). A cycle (G,c) is called proper if any two adjacent have distinct colors. An n≥3 properly vertex-pancyclic each contained in length ℓ for every 3≤ℓ≤n. Fujita Magnant conjectured that complete δc(G)≥n+12 vertex-pancyclic. Chen, Huang Yuan part...

colors as a key element of emotional (sentimental) impacts and interaction with its surrounding, which is the most important visual factor, has had a great importance in the history of art and culture of iran for decades. this key element has shown its importance in several historical monuments and buildings. a large number of color theoreticians believe that colors affect the human beings’ spi...

For p∈N, a coloring λ of the vertices graph G is p-centered if for every connected subgraph H G, either receives more than p colors under or there color that appears exactly once in H. Centered colorings play an important role theory sparse classes introduced by Nešetřil and Ossona de Mendez [31], [32], as they structurally characterize bounded expansion — one key sparsity notions this theory. ...

Let H be a fixed graph on k vertices. For an edge-coloring c of H , we say that H is rainbow, or totally multicolored if c assigns distinct colors to all edges of H . We show, that it is easy to avoid rainbow induced graphs H . Specifically, we prove that for any graph H (with some notable exceptions), and for any graphs G, G 6= H , there is an edge-coloring of G with k colors which contains no...

this study focused on the role of appropriate equivalence selection of colors in the field of advanced pranic healing (aph), based on mona baker’s equivalence, both at word level and above word level. the partici- pants included 40 bachelor’s students studying in the field of english translation. participants received the colors’ translation test (ctt) included in the book “advanced pranic heal...

A mixed hypergraph is a triple H = (X, C,D), where X is the vertex set and each of C, D is a family of subsets of X, the C-edges and D-edges, respectively. A proper k-coloring of H is a mapping c : X → [k] such that each C-edge has two vertices with a common color and each D-edge has two vertices with distinct colors. Upper chromatic number is the maximum number of colors that can be used in a ...

A total coloring of a graph G is to color all vertices and edges of G so that no two adjacent or incident elements receive the same color. Let C be a set of colors, and let ω be a cost function which assigns to each color c in C a real number ω(c) as a cost of c. A total coloring f of G is called an optimal total coloring if the sum of costs ω( f (x)) of colors f (x) assigned to all vertices an...