Displaying similar documents to “A Degree Condition Implying Ore-Type Condition for Even [2,b]-Factors in Graphs”

F -continuous graphs

Gary Chartrand, Elzbieta B. Jarrett, Farrokh Saba, Ebrahim Salehi, Ping Zhang (2001)

Czechoslovak Mathematical Journal

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For a nontrivial connected graph F , the F -degree of a vertex v in a graph G is the number of copies of F in G containing v . A graph G is F -continuous (or F -degree continuous) if the F -degrees of every two adjacent vertices of G differ by at most 1. All P 3 -continuous graphs are determined. It is observed that if G is a nontrivial connected graph that is F -continuous for all nontrivial connected graphs F , then either G is regular or G is a path. In the case of a 2-connected graph F , however,...

Note on independent sets of a graph

Jaroslav Ivančo (1994)

Mathematica Bohemica

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Let the number of k -element sets of independent vertices and edges of a graph G be denoted by n ( G , k ) and m ( G , k ) , respectively. It is shown that the graphs whose every component is a circuit are the only graphs for which the equality n ( G , k ) = m ( G , k ) is satisfied for all values of k .

Degree-continuous graphs

John Gimbel, Ping Zhang (2001)

Czechoslovak Mathematical Journal

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A graph G is degree-continuous if the degrees of every two adjacent vertices of G differ by at most 1. A finite nonempty set S of integers is convex if k ∈ S for every integer k with min ( S ) ≤ k ≤ max ( S ) . It is shown that for all integers r > 0 and s ≥ 0 and a convex set S with min ( S ) = r and max ( S ) = r + s , there exists a connected degree-continuous graph G with the degree set S and diameter 2 s + 2 . The minimum order of a degree-continuous graph with a prescribed degree set is studied. Furthermore, it is shown that for every graph G and convex...

The Degree-Diameter Problem for Outerplanar Graphs

Peter Dankelmann, Elizabeth Jonck, Tomáš Vetrík (2017)

Discussiones Mathematicae Graph Theory

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For positive integers Δ and D we define nΔ,D to be the largest number of vertices in an outerplanar graph of given maximum degree Δ and diameter D. We prove that [...] nΔ,D=ΔD2+O (ΔD2−1) n Δ , D = Δ D 2 + O Δ D 2 - 1 is even, and [...] nΔ,D=3ΔD−12+O (ΔD−12−1) n Δ , D = 3 Δ D - 1 2 + O Δ D - 1 2 - 1 if D is odd. We then extend our result to maximal outerplanar graphs by showing that the maximum number of vertices in a maximal outerplanar graph of maximum degree Δ and diameter D asymptotically equals nΔ,D.

Results on F -continuous graphs

Anna Draganova (2009)

Czechoslovak Mathematical Journal

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For any nontrivial connected graph F and any graph G , the of a vertex v in G is the number of copies of F in G containing v . G is called if and only if the F -degrees of any two adjacent vertices in G differ by at most 1; G is if the F -degrees of all vertices in G are the same. This paper classifies all P 4 -continuous graphs with girth greater than 3. We show that for any nontrivial connected graph F other than the star K 1 , k , k ≥ 1 , there exists a regular graph that is not F -continuous. If...