What question did this study set out to answer?

The aim is to establish conditions under which certain graphs exhibit factor properties, particularly focusing on critical graphs and avoidable graphs.

June 13, 2026

Existence theorems on star-factor deleted (critical) graph and critical avoidable graphs

Puntos clave

The aim is to establish conditions under which certain graphs exhibit factor properties, particularly focusing on critical graphs and avoidable graphs.
Proving existence theorems for star-factor deleted and critical graphs based on binding number and toughness.
Constructing extremal graphs to demonstrate the best possible bounds for the defined properties.
Demonstrated that specific configurations lead to the existence of k-factor critical graphs and k-factor deleted graphs.
Identified conditions for graphs to be k-factor critical avoidable based on toughness metrics.

Resumen

Let Formula: see text be a graph, let Formula: see text be an integer and let Formula: see text = Formula: see text. A Formula: see text-factor of Formula: see text is a spanning subgraph of Formula: see text, in which each component is isomorphic to a member in Formula: see text. Let Formula: see text, Formula: see text and Formula: see text be three nonnegative integers. For any Formula: see text with Formula: see text, assume Formula: see text has a Formula: see text-factor, then Formula: see text is a Formula: see text-factor critical graph. For any Formula: see text with Formula: see text, assume Formula: see text has a Formula: see text-factor, then Formula: see text is a Formula: see text-factor deleted graph. For any Formula: see text with Formula: see text and any Formula: see text, assume Formula: see text contains a Formula: see text-factor, then Formula: see text is Formula: see text-factor critical avoidable. In this paper, we obtain existence theorems on a Formula: see text-factor deleted graph(Formula: see text-factor critical graph) is regarding the binding number and a Formula: see text-factor critical avoidable graph is regarding the tight toughness and the isolated toughness for a graph, respectively. Furthermore, by constructing extremal graphs, we show that the bounds are best possible.

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Cite This Study

Ren et al. (Fri,) studied this question.

synapsesocial.com/papers/6a2cf551faef96ed7f057580 https://doi.org/https://doi.org/10.1142/s1793830926500692

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