Displaying similar documents to “Independent face and vertex covers in plane graphs”

Arithmetically maximal independent sets in infinite graphs

Stanisław Bylka (2005)

Discussiones Mathematicae Graph Theory

Similarity:

Families of all sets of independent vertices in graphs are investigated. The problem how to characterize those infinite graphs which have arithmetically maximal independent sets is posed. A positive answer is given to the following classes of infinite graphs: bipartite graphs, line graphs and graphs having locally infinite clique-cover of vertices. Some counter examples are presented.

On infinite outerplanar graphs

Luis B. Boza, Ana Diánez, Alberto Márquez (1994)

Mathematica Bohemica

Similarity:

In this Note, we study infinite graphs with locally finite outerplane embeddings, given a characterization by forbidden subgraphs.

The crossing numbers of join products of paths with graphs of order four

Marián Klešč, Stefan Schrötter (2011)

Discussiones Mathematicae Graph Theory

Similarity:

Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numbers of graphs obtained as join product of two graphs. In the paper, the exact values of crossing...

Light Graphs In Planar Graphs Of Large Girth

Peter Hudák, Mária Maceková, Tomáš Madaras, Pavol Široczki (2016)

Discussiones Mathematicae Graph Theory

Similarity:

A graph H is defined to be light in a graph family 𝒢 if there exist finite numbers φ(H, 𝒢) and w(H, 𝒢) such that each G ∈ 𝒢 which contains H as a subgraph, also contains its isomorphic copy K with ΔG(K) ≤ φ(H, 𝒢) and ∑x∈V(K) degG(x) ≤ w(H, 𝒢). In this paper, we investigate light graphs in families of plane graphs of minimum degree 2 with prescribed girth and no adjacent 2-vertices, specifying several necessary conditions for their lightness and providing sharp bounds on φ and w...

On H-Irregularity Strength Of Graphs

Faraha Ashraf, Martin Bača, Marcela Lascśaková, Andrea Semaničová-Feňovčíková (2017)

Discussiones Mathematicae Graph Theory

Similarity:

New graph characteristic, the total H-irregularity strength of a graph, is introduced. Estimations on this parameter are obtained and for some families of graphs the precise values of this parameter are proved.

Characterizations of planar plick graphs

V.R. Kulli, B. Basavanagoud (2004)

Discussiones Mathematicae Graph Theory

Similarity:

In this paper we present characterizations of graphs whose plick graphs are planar, outerplanar and minimally nonouterplanar.

Radio Graceful Hamming Graphs

Amanda Niedzialomski (2016)

Discussiones Mathematicae Graph Theory

Similarity:

For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio...

The Thickness of Amalgamations and Cartesian Product of Graphs

Yan Yang, Yichao Chen (2017)

Discussiones Mathematicae Graph Theory

Similarity:

The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study...