## Abstract A vertex set __Y__ in a (hyper)graph is called __k__‐independent if in the sub(hyper)‐graph induced by __Y__ every vertex is incident to less than __k__ edges. We prove a lower bound for the maximum cardinality of a __k__‐independent set—in terms of degree sequences—which strengthens an
Lower bounds on size and independence inK4-free graphs
✍ Scribed by Fraughnaugh, Kathryn L.; Locke, Stephen C.
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 131 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0364-9024
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✦ Synopsis
We investigate lower bounds on the size of K 4 -free graphs. For several ranges of independence relative to order and for graphs with maximum degree 3 and 4, we find sharp lower bounds. We also evaluate Ramsey-type numbers over the classes of graphs with maximum degree 3 and with maximum degree 4.
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## Abstract In this paper, by applying the discharging method, we obtain new lower bounds for the size of edge chromatic critical graphs for small maximum degree Δ. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 81–92, 2004
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