Demonstrates new bounds on the vertex cover number in graphs, highlighting specific graph types with implications for graph theory.
This paper presents tight bounds and characterizations for the vertex cover number and the connected vertex cover number of graphs. In particular, we identify all graphs for which βc(G) = |V (G)| − 1, proving that these are exactly the cycles and complete graphs. The analysis employs tools such as the degree matrix and the Rayleigh quotient to derive new and sharp upper bounds.
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Mirasheh et al. (2026) studied this question.
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