Let G be a simple undirected connected graph on n vertices with maximum degree Δ.
Brooks' Theorem states that G has a proper Δ‐coloring unless G is a complete graph, or a …

We continue research into a well-studied family of problems that ask if the vertices of a graph
can be partitioned into sets A and B, where A is an independent set and B induces a graph …

Let G be a connected graph with maximum degree Δ≥ 3 distinct from K Δ+ 1. Generalizing
Brooks' Theorem, Borodin and independently Bollobás and Manvel, proved that if p 1,…, ps …

As an extension of the Brooks theorem, Catlin in 1979 showed that if H is neither an odd
cycle nor a complete graph with maximum degree Δ (H), then H has a vertex Δ (H)-coloring …

Dirac's theorem on chordal graphs implies Brooks' theorem - ScienceDirect Skip to main
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We continue research into a well‐studied family of problems that ask whether the vertices of
a given graph can be partitioned into sets A and B, where A is an independent set and B …

Brooks' Theorem from 1941 is a cornerstone in graph theory. Until then graph coloring
theory was centered around planar graphs and the four color problem. Brooks' Theorem was …

In 2007 Matamala proved that if $ G $ is a simple graph with maximum degree $\Delta\geq
3$ not containing $ K_ {\Delta+ 1} $ as a subgraph and $ s, t $ are positive integers such that …

For a given graph $ H $ and the graphical properties $ P_1, P_2,\ldots, P_k $, we say the
graph $ H $ has a $(V_1, V_2,\ldots, V_k) $-decomposition, if for each $ i\in [k] $, the …

In 1940, a certain William T. TUTTE presented the Cambridge Philosophical Society a paper
called “Coloring of abstract graphs”; authored by Rowland L. BROOKS. In this paper, he …