منابع مشابه
K4-free graphs with no odd holes
All K4-free graphs with no odd hole and no odd antihole are three-colourable, but what about K4free graphs with no odd hole? They are not necessarily three-colourable, but we prove a conjecture of Ding that they are all four-colourable. This is a consequence of a decomposition theorem for such graphs; we prove that every such graph either has no odd antihole, or belongs to one of two explicitly...
متن کاملEven-cycle decompositions of graphs with no odd-K4-minor
An even-cycle decomposition of a graph G is a partition of E(G) into cycles of even length. Evidently, every Eulerian bipartite graph has an even-cycle decomposition. Seymour (1981) proved that every 2-connected loopless Eulerian planar graph with an even number of edges also admits an even-cycle decomposition. Later, Zhang (1994) generalized this to graphs with no K5-minor. Our main theorem gi...
متن کاملColoring Clean and K4-free Circle Graphs
A circle graph is the intersection graph of chords drawn in a circle. The best known general upper bound on the chromatic number of circle graphs with clique number k is 50 · 2. We prove a stronger bound of 2k − 1 for graphs in a simpler subclass of circle graphs, so called clean graphs. Based on this result we prove that the chromatic number of every circle graph with clique number at most 3 i...
متن کاملColoring (P6, diamond, K4)-free graphs
We show that every (P6, diamond, K4)-free graph is 6-colorable. Moreover, we give an example of a (P6, diamond, K4)-free graph G with χ(G) = 6. This generalizes some known results in the literature.
متن کاملList-coloring graphs without K4, k-minors
In this note, it is shown that every graph with no K4,k-minor is 4k-list-colorable. We also give an extremal function for the existence for a K4,k-minor. Our proof implies that there is a linear time algorithm for showing that either G has a K4,k-minor or G is 4k-choosable. In fact, if the latter holds, then the algorithm gives rise to a 4k-list-coloring. © 2008 Elsevier B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00090-3