A note on Berge–Fulkerson coloring
نویسندگان
چکیده
منابع مشابه
A note on Berge-Fulkerson coloring
The Berge–Fulkerson Conjecture states that every cubic bridgeless graph has six perfect matchings such that every edge of the graph is contained in exactly two of these perfect matchings. In this paper, a useful technical lemma is proved that a cubic graph G admits a Berge–Fulkerson coloring if and only if the graph G contains a pair of edge-disjoint matchings M1 and M2 such that (i) M1 ∪ M2 in...
متن کاملA Note on Linear Coloring of Graphs
A proper vertex coloring of a graph is called linear if the subgraph induced by the vertices colored by any two colors is a set of vertex-disjoint paths. The linear chromatic number of a graph G, denoted by lc(G), is the minimum number of colors in a linear coloring of G. Extending a result of Alon, McDiarmid and Reed concerning acyclic graph colorings, we show that if G has maximum degree d th...
متن کاملA Note on the Road-Coloring Conjecture
Some results relating to the road-coloring conjecture of Alder, Goodwyn, and Weiss, which give rise to an O(n2) algorithm to determine whether or not a given edge-coloring of a graph is a road-coloring, are noted. Probabilistic analysis is then used to show that, if the outdegree of every edge in an n-vertex digraph is δ = ω(logn), a road-coloring for the graph exists. An equivalent re-statemen...
متن کاملA Note on Harmonious Coloring of Caterpillars
The harmonious coloring of an undirected simple graph is a vertex coloring such that adjacent vertices are assigned different colors and each pair of colors appears together on at most one edge. The harmonious chromatic number of a graph is the least number of colors used in such a coloring. The harmonious chromatic number of a path is known, whereas the problem to find the harmonious chromatic...
متن کاملA note on partial list coloring
Let G be a simple graph with n vertices and list chromatic number χl(G) = χl. Suppose that 0 ≤ t ≤ χl and each vertex of G is assigned a list of t colors. Albertson, Grossman and Haas [1] conjectured that at least tn χl vertices of G can be colored from these lists. In this paper we find some new results in partial list coloring which help us to show that the conjecture is true for at least hal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.12.024