On almost (k-1)-degenerate (k+1)-chromatic graphs and hypergraphs
نویسنده
چکیده
Recall that a (hyper)graph is d-degenerate if every of its nonempty subgraphs has a vertex of degree at most d. Every d-degenerate (hyper)graph is (easily) (d + 1)colorable. A (hyper)graph is almost d-degenerate if it is not d-degenerate, but every its proper subgraph is d-degenerate. In particular, if G is almost (k − 1)-degenerate, then after deleting any edge it is k-colorable. For k ≥ 2, we study properties of almost (k − 1)-degenerate (hyper)graphs that are not k-colorable. By definition, each such (hyper)graph is (k + 1)-critical.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 313 شماره
صفحات -
تاریخ انتشار 2013