Displaying similar documents to “On local structure of 1-planar graphs of minimum degree 5 and girth 4”

On ( 4 , 1 ) * -choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles

Haihui Zhang (2013)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A graph G is called ( k , d ) * -choosable if for every list assignment L satisfying | L ( v ) | = k for all v ∈ V ( G ) , there is an L -coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this paper, it is proved that every toroidal graph without chordal 7-cycles and adjacent 4-cycles is ( 4 , 1 ) * -choosable.

Paths with restricted degrees of their vertices in planar graphs

Stanislav Jendroľ (1999)

Czechoslovak Mathematical Journal

Similarity:

In this paper it is proved that every 3 -connected planar graph contains a path on 3 vertices each of which is of degree at most 15 and a path on 4 vertices each of which has degree at most 23 . Analogous results are stated for 3 -connected planar graphs of minimum degree 4 and 5 . Moreover, for every pair of integers n ≥ 3 , k ≥ 4 there is a 2 -connected planar graph such that every path on n vertices in it has a vertex of degree k .

Join of two graphs admits a nowhere-zero 3 -flow

Saieed Akbari, Maryam Aliakbarpour, Naryam Ghanbari, Emisa Nategh, Hossein Shahmohamad (2014)

Czechoslovak Mathematical Journal

Similarity:

Let G be a graph, and λ the smallest integer for which G has a nowhere-zero λ -flow, i.e., an integer λ for which G admits a nowhere-zero λ -flow, but it does not admit a ( λ - 1 ) -flow. We denote the minimum flow number of G by Λ ( G ) . In this paper we show that if G and H are two arbitrary graphs and G has no isolated vertex, then Λ ( G ∨ H ) ≤ 3 except two cases: (i) One of the graphs G and H is K 2 and the other is 1 -regular. (ii) H = K 1 and G is a graph with at least one isolated vertex or a component whose every...

On integral sum graphs with a saturated vertex

Zhibo Chen (2010)

Czechoslovak Mathematical Journal

Similarity:

As introduced by F. Harary in 1994, a graph G is said to be an i n t e g r a l s u m g r a p h if its vertices can be given a labeling f with distinct integers so that for any two distinct vertices u and v of G , u v is an edge of G if and only if f ( u ) + f ( v ) = f ( w ) for some vertex w in G . We prove that every integral sum graph with a saturated vertex, except the complete graph K 3 , has edge-chromatic number equal to its maximum degree. (A vertex of a graph G is said to be if it is adjacent to every...

Vertex-disjoint stars in graphs

Katsuhiro Ota (2001)

Discussiones Mathematicae Graph Theory

Similarity:

In this paper, we give a sufficient condition for a graph to contain vertex-disjoint stars of a given size. It is proved that if the minimum degree of the graph is at least k+t-1 and the order is at least (t+1)k + O(t²), then the graph contains k vertex-disjoint copies of a star K 1 , t . The condition on the minimum degree is sharp, and there is an example showing that the term O(t²) for the number of uncovered vertices is necessary in a sense.

Results on F -continuous graphs

Anna Draganova (2009)

Czechoslovak Mathematical Journal

Similarity:

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...