On Large Chromatic Graphs Not Containing Prescribed Subgraphs
A. Hajnal (1985)
Publications du Département de mathématiques (Lyon)
Similarity:
A. Hajnal (1985)
Publications du Département de mathématiques (Lyon)
Similarity:
Robert Janczewski, Michał Małafiejski, Anna Małafiejska (2018)
Discussiones Mathematicae Graph Theory
Similarity:
Csilla Bujtás, Zsolt Tuza (2016)
Discussiones Mathematicae Graph Theory
Similarity:
A K3-WORM coloring of a graph G is an assignment of colors to the vertices in such a way that the vertices of each K3-subgraph of G get precisely two colors. We study graphs G which admit at least one such coloring. We disprove a conjecture of Goddard et al. [Congr. Numer. 219 (2014) 161-173] by proving that for every integer k ≥ 3 there exists a K3-WORM-colorable graph in which the minimum number of colors is exactly k. There also exist K3-WORM colorable graphs which have a K3-WORM...
Halina Bielak (1998)
Discussiones Mathematicae Graph Theory
Similarity:
In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.
Mieczysław Borowiecki, Anna Fiedorowicz (2006)
Discussiones Mathematicae Graph Theory
Similarity:
In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement,...
Halina Bielak (1999)
Discussiones Mathematicae Graph Theory
Similarity:
We give a lower bound for the Ramsey number and the planar Ramsey number for C₄ and complete graphs. We prove that the Ramsey number for C₄ and K₇ is 21 or 22. Moreover we prove that the planar Ramsey number for C₄ and K₆ is equal to 17.
Tomáš Vetrík (2012)
Discussiones Mathematicae Graph Theory
Similarity:
The choice number of a graph G is the smallest integer k such that for every assignment of a list L(v) of k colors to each vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from L(v). We present upper and lower bounds on the choice number of complete multipartite graphs with partite classes of equal sizes and complete r-partite graphs with r-1 partite classes of order two.
Farrell, E.J. (1981)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Brandt, Stephan, Brinkmann, Gunnar, Harmuth, Thomas (1998)
The Electronic Journal of Combinatorics [electronic only]
Similarity:
Krzysztof Turowski (2015)
Discussiones Mathematicae Graph Theory
Similarity:
For a graph G with a given subgraph H, the backbone coloring is defined as the mapping c : V (G) → N+ such that |c(u) − c(v)| ≥ 2 for each edge {u, v} ∈ E(H) and |c(u) − c(v)| ≥ 1 for each edge {u, v} ∈ E(G). The backbone chromatic number BBC(G,H) is the smallest integer k such that there exists a backbone coloring with maxv∈V (G) c(v) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.
DeLaVina, Ermelinda, Fajtlowicz, Siemion (1996)
The Electronic Journal of Combinatorics [electronic only]
Similarity:
Jaroslav Nešetřil (1973)
Časopis pro pěstování matematiky
Similarity:
José D. Alvarado, Simone Dantas, Dieter Rautenbach (2017)
Discussiones Mathematicae Graph Theory
Similarity:
For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination in graphs, Discrete Appl. Math. 161 (2013) 806-812] present some kind of characterization of the graphs G for which R(G) − yr2(G) = k for some integer k. Unfortunately, their result does not lead to an algorithm that allows to recognize...
Oleg V. Borodin, Anna O. Ivanova (2012)
Discussiones Mathematicae Graph Theory
Similarity:
The trivial lower bound for the 2-distance chromatic number χ₂(G) of any graph G with maximum degree Δ is Δ+1. It is known that χ₂ = Δ+1 if the girth g of G is at least 7 and Δ is large enough. There are graphs with arbitrarily large Δ and g ≤ 6 having χ₂(G) ≥ Δ+2. We prove the 2-distance 4-colorability of planar subcubic graphs with g ≥ 22.
Kubicka, Ewa (2004)
International Journal of Mathematics and Mathematical Sciences
Similarity:
John Mitchem, Patrick Morriss, Edward Schmeichel (1997)
Discussiones Mathematicae Graph Theory
Similarity:
We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost chromatic number of maximal outerplanar and maximal planar graphs can be arbitrarily large and...
Jan Kratochvíl (1995)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
In this note, we introduce the notion of -Ramsey classes of graphs and we reveal connections to intersection dimensions of graphs.