Multi-coloring problem is a generalization of the well known Graph coloring problem which is known to be NP-hard. Multi-coloring problem can be solved by algorithms designed for the graph coloring problem after transformation of the graphs. However, since the graph transformations increase the size and order of the given graph, in some cases, it may be impractical to solve multi-coloring proble...

Vertex coloring of a graph is the assignment of labels to the vertices of the graph so that adjacent vertices have different labels. In the case of polyhedral graphs, the chromatic number is 2, 3, or 4. Edge coloring problem and face coloring problem can be converted to vertex coloring problem for appropriate polyhedral graphs. We have been developed an interactive learning system of polyhedra,...

We consider a multiagent extension of single-agent graph coloring. Multiple agents hold disjoint autonomous subgraphs of a global graph, and every color used by the agents in coloring the graph has associated cost. In this multiagent graph coloring scenario, we seek a minimum legal coloring of the global graph’s vertices, such that the coloring is also Pareto efficient, socially fair, and indiv...

In the paper we consider the complexity of constructing optimal policies (strategies) for some type of partially observed Markov decision processes. This particular case of the classical problem deals with nite stationary processes, and can be represented as constructing optimal strategies to reach target vertices from a starting vertex in a graph with colored vertices and probabilistic deviati...

A mixed hypergraph is a tripleH = (X, C,D), whereX 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 an injective mapping c : X → {1, . . . , k} such that each C-edge has two vertices with a common color and each D-edge has two vertices with distinct colors. Maximum number of colors in a coloring using all the colo...

In this paper we consider the class of simple graphs defined by excluding, as induced subgraphs, even holes (i.e., chordless cycles of even length) and diamonds (i.e., a graph obtained from a clique of size 4 by removing an edge). We say that such graphs are (evenhole, diamond)-free. For this class of graphs we first obtain a decomposition theorem, using clique cutsets, bisimplicial cutsets (wh...

Sport scheduling is a trending research topic in operations research. Local search heuristics are among the most effective methods to construct schedules. Prior studies have noted the existance of non-connectivity in neighborhoods used in local search heuristics for single round-robin tournament scheduling. This non-connectivity affects the performance of local search heuristics. It is well-kno...

This paper is motivated by the problem of finding the largest single-deletion-correcting code for binary strings. The Varshamov–Tenengolts construction classifies binary strings into non-overlapping sets, the largest set of these is asymptotically the largest singledeletion-correcting code. However despite the asymptotic optimality little is known about the quality of the construction as a func...

A new way of constructing (minimal) perfect hash functions is described. The technique considerably reduces the overhead associated with resolving buckets in two-level hashing schemes. Evaluating a hash function requires just one multiplication and a few additions apart from primitive bit operations. The number of accesses to memory is two, one of which is to a fixed location. This improves the...

We consider the problem of covering the complete r-uniform hypergraphs on n vertices using complete r-partite graphs. We obtain lower bounds on the size of such a covering. For small values of r our result implies a lower bound of Ω( e r r √ r n log n) on the size of any such covering. This improves the previous bound of Ω(rn log n) due to Snir [5]. We also obtain good lower bounds on the size ...