- Tytuł:
- A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs
- Autorzy:
-
Zhou, Sizhong
Yang, Fan
Sun, Zhiren - Tematy:
-
graph
minimum degree
neighborhood
fractional [a
b]-factor
fractional ID-[a
b]-factor-critical graph - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/31340936.pdf Link otwiera się w nowym oknie
- Opis:
- Let $G$ be a graph of order $n$, and let $a$ and $b$ be two integers with $ 1 \le a \le b $. Let $ h : E(G) \rightarrow [0, 1] $ be a function. If \( a \le \Sigma_{ e \ni x } h(e) \le b \) holds for any $ x \in V (G) $, then we call $ G[F_h] $ a fractional $ [a, b] $-factor of $ G $ with indicator function $ h $, where $ F_h = \{ e \in E(G) : h(e) > 0 \} $. A graph $G$ is fractional independent-set-deletable $[a, b]$-factor-critical (in short, fractional ID-$[a, b]$-factor-critical) if $ G − I $ has a fractional $ [a, b] $-factor for every independent set $I$ of $G$. In this paper, it is proved that if $ n \ge \frac{(a+2b)(2a+2b-3)+1}{b} $, $ \delta (G) \ge \frac{bn}{a+2b} + a $ and $ | N_G(x) \cup N_G(y) | \ge \frac{(a+b)n}{a+2b} $ for any two nonadjacent vertices $ x, y \in V (G) $, then $ G $ is fractional ID-$[a, b]$-factor-critical. Furthermore, it is shown that this result is best possible in some sense.
- Dostawca treści:
- Biblioteka Nauki
Artykuł