Abstract Graph Factors and Matching Extensions deals with two important branches of graph
theory-factor theory and extendable graphs. Due to the mature techniques and wide ranges …

Let ℋ be a set of graphs. A graph G is said to be ℋ‐free if G does not contain H as an
induced subgraph for all H in ℋ, and we call ℋ a forbidden pair if∣ ℋ∣= 2. In 2008, Faudree …

Let H be a set of graphs. A graph G is said to be H-free if G does not contain H as an
induced subgraph for all H∈ H, and we call H a forbidden pair if| H|= 2. A graph is called …

A cycle C in a graph G is called dominating if every edge of G is incident with a vertex of C.
For a set H of connected graphs, a graph G is said to be H-free if G does not contain any …

In this paper, we consider forbidden subgraphs which force the existence of a 2-factor. Let
equation image be the class of connected graphs of minimum degree at least two and …

In this paper, we characterize 2-connected {K 1, 3, N 3, 1, 1}-free graphs without Hamiltonian
cycle, where K 1, 3 is the star of order 4 and N n 1, n 2, n 3 is the graph obtained from K 3 …

In this paper, we consider pairs of forbidden subgraphs that imply the existence of a 2-factor
in a graph. For d≥ 2, let d be the set of connected graphs of minimum degree at least d. Let …

PROOF TECHNIQUES FOR FACTOR THEOREMS YOSHIMI EGAWA Page 1 SOlYAI
SOCIETY MATHEMATICAL STUDIES. 17 Horizons of Combinatorics Balatonalmadi pp.67-78 …

If is a subclass of the class of claw‐free graphs, then is said to be stable if, for any, the local
completion of G at any vertex is also in. If is a closure operation that turns a claw‐free graph …

For an integer k with k≥ 2 and a pair of connected graphs F1 and F2 of order at least three,
we say that {F1, F2} is a k-forbidden pair if every k-connected {F1, F2}-free graph, except …