A graphG is 3-colorable if and only if it maps homomorphically to the complete 3-vertex graph K3. The last condition can be checked by a k-consistency algorithm where the parameter k has to be chosen large enough, dependent on G. Let W (G) denote the minimum k sufficient for this purpose. For a non3-colorable graph G, W (G) is equal to the minimum k such that G can be distinguished from K3 in t...

Given a graph G, an edge-coloring or G with colors 1,2.3.. is consecutive if the colors of edges incident to each vertex fomm an interval of integer-s. This papelis devoted to bipartite graphs which do not have such a coloring of edges. We investigate their consecutive coloring deficiency, or shortly the deficiency d(G) of G, i.e. the minimum number of pendant edges whose attachment to G makes ...

According to Bradbury and Mather (2009), in the 2003-2004 academic school year 45% of new students enrolling in four-year institutions were first-generation students. When compared to continuing-generation college students, first-generation students have been shown to find the college going experience to be more stressful (Phinney & Haas, 2003). Despite the knowledge that these students find th...

Based on the notions of locality and recognizability for n-dimensional languages n-dimensionally colorable 1-dimensional languages are introduced. It is shown: A language L is in NP if and only if L is n-dimensionally colorable for some n. An analogous characterization in terms of deterministic n-dimensional colorability is obtained for P. The addition of one unbounded dimension for coloring le...

Planar graphs without 3-cycles at distance less than 4 and without 5-cycles are proved to be 3-colorable. We conjecture that, moreover, each plane graph with neither 5-cycles nor intersecting 3-cycles is 3-colorable. In this conjecture, none of the two assumptions can be dropped because there exist planar 4-chromatic graphs without 5-cycles, as well as planar 4chromatic graphs without intersect...

J.BSTllCT It is well-known that the problem of determining whether a planar map is three-colorable is NP-complete. There are also several isolated results on three-colorability for certain classes of maps. Herein, we consider. a new class of maps that consists of those involving lines and half-lines. It is shown that such maps are three-colorable if they satisfy a simple condition. An extension...

Warning sounds are necessary to promptly alert workers of events that can compromise safety. A wide range of strategies, including verbal and non-verbal signals have been used in different environments (Edworthy & Adams 1996; Haas & Edworthy 2006; Edworthy & Hellier 2006). Unfortunately, the use of warning signals in industry is often submitted to intuitive installation practices with little re...