Some anonymous opinions about mixed hypergraph coloring

Last Updated November 24, 2006 by Vitaly Voloshin

...mixed hypergraph coloring is NOT INTERESTING because it has no analogy with graph coloring...

...mixed hypergraph coloring is ESPECIALLY INTERESTING because it has no analogy with graph coloring...

...the notion of C-edge is unnatural and artificial...

...the notion of C-edge is quite natural...

...no doubts, chromatic spectrum is continuous...

... you will see, the chromatic spectrum is broken...

...what the devil, if the structure is less trivial, more interesting and beautiful, then it gets uncolorable...

...it looks like coloring theory becomes the theory of uncolorable mixed hypergraphs, and colorability seems to be an island in a darkness...

... what is a color? - Nobody knows...

...all this stuff is not for use in painting .... (the opinion of a professional painter)

...who knows, may be eventually this stuff will be used somehow in painting .... (the opinion of a professional mathematician)

... the paper where you define the upper chromatic number, lacks focus...

... I am a "general" graph theorist. My initial reaction to the concept of mixed hypergraphs was somewhat negative. In particular, I felt that C-edges were slightly contrived and I doubted whether I, or many other graph theorists would become interested in this concept. As my reading progressed, I found that I was becoming more interested in mixed hypergraphs ...

... all generalizations of coloring came out from graph coloring where problem for the maximum number of colors does not exist at all. In context of mixed hypergraphs, it is the only such case. This means that previous generalizations of coloring came out from this unique asymmetric case...

...all my life I worked in coloring and never heard about mixed hypergraphs. It was a surprise for me to realize that I worked in mixed hypergraphs ....

... sorry, I don't understand this... I have a feeling like among the trees I don't see the forest ...

... the uncolorability looks like an expanded zero, the measure of uncolorability looks like we reach the back of the beyond...

... you should take Hegel as a coauthor of your paper about mixed hypergraphs...

... oh, god, why did you hide the natural number at the very bottom of uncolorability?...

...there is nothing new in mixed hypergraphs since these colorings can be reduced to graph colorings like hypergraphs can be reduced to bipartite graphs...

... the difference between C-edges and D-edges is like the difference between man and woman: much is the same but some small and significant is different. Otherwise, why females have two copies of the X chromosome, i.e. the X - X pair (C-edge?) while males have one X chromosome and one Y chromosome (D-edge?), but all the remaining chromosomes are identical?...

... I don't understand what is the same and what is different in this world. Please give me exact definitions...

... each human being is simply a quantum of time of existence of an integral discrete system which is called "human population". Its superior goal is to achieve the longest lifetime which is expressing in universal saving of time through science, industry, money...

... coloring theory would be insignificant if it would not be a theory of set partitions avoiding conflicts...

"All men are the same while all women are different..." (a woman's joke related to colorings)
CLAIM: "... All your stuff about contradictions is nothing but a thought, an idea..."
ANSWER: "-- No. Just look at the nearest person of opposite sex -- and you will find that it is a reality..."

The relation between Graph Coloring and Mixed Hypergraph Coloring is similar to relation between natural numbers and all integers. Natural numbers do not have 0, Graph Coloring does not have uncolorability. Interaction of positive and negative integeres looks like interaction of C-edges and D-edges.

COBASE (1997) and NSF (2004) opinions.