Graph coloring with cardinality constraints on the neighborhoods

Graph Coloring with Local and Global Constraints Graph Coloring with Local and Global Constraints

Coloring Graphs with Sparse Neighborhoods

It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d/f is at most O(d/ log f). This is tight (up to a constant factor) for all admissible values of d and f .

Coloring Graphs with Dense Neighborhoods

It is shown that any graph with maximum degree ∆ in which the average degree of the induced subgraph on the set of all neighbors of any vertex exceeds 6k 2 6k2+1 ∆ + k+ 6 is either (∆ − k)-colorable or contains a clique on more than ∆ − 2k vertices. In the k = 1 case we improve the bound on the average degree to 2 3∆ + 4 and the bound on the clique number to ∆ − 1. As corollaries, we show that ...

Automatic Service Composition Based on Graph Coloring

Web services as independent software components are published on the Internet by service providers and services are then called by users’ request. However, in many cases, no service alone can be found in the service repository that could satisfy the applicant satisfaction. Service composition provides new components by using an interactive model to accelerate the programs. Prior to service comp...

dynamic coloring of graph

در این پایان نامه رنگ آمیزی دینامیکی یک گراف را بیان و مطالعه می کنیم. یک –kرنگ آمیزی سره ی رأسی گراف g را رنگ آمیزی دینامیکی می نامند اگر در همسایه های هر رأس v?v(g) با درجه ی حداقل 2، حداقل 2 رنگ متفاوت ظاهر شوند. کوچکترین عدد صحیح k، به طوری که g دارای –kرنگ آمیزی دینامیکی باشد را عدد رنگی دینامیکی g می نامند و آنرا با نماد ?_2 (g) نمایش می دهند. مونت گمری حدس زده است که تمام گراف های منتظم ...