Some Remarks on the Simultaneous Chromatic Number
暂无分享，去创建一个
We present several partial results, variants, and
consistency results concerning the following (as yet unsolved)
conjecture. If X is a graph
on the ground set V with
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaafeart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn
% 2BKvginnfarmqr1ngBPrgitLxBI9gBamXvP5wqSXMqHnxAJn0BKvgu
% HDwzZbqegm0B1jxALjhiov2DaeHbuLwBLnhiov2DGi1BTfMBaebbnr
% fifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0xc9
% pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFv
% e9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaakeaacaWGdbGa
% amiAaiaadkhadaqadaqaaiaadIfaaiaawIcacaGLPaaacqGH9aqpcq
% GH1ecWdaWgaaWcbaGaaGymaaqabaaaaa!4C54!$$
Chr{\left( X \right)} = {\aleph }_{1}
$$ then
X has an edge coloring
F with
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaafeart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn
% 2BKvginnfarmqr1ngBPrgitLxBI9gBamXvP5wqSXMqHnxAJn0BKvgu
% HDwzZbqegm0B1jxALjhiov2DaeHbuLwBLnhiov2DGi1BTfMBaebbnr
% fifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0xc9
% pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFv
% e9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaakeaacqGH1ecW
% daWgaaWcbaGaaGymaaqabaaaaa!463C!$$
{\aleph }_{1}
$$ colors such that if
V is decomposed into
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaafeart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn
% 2BKvginnfarmqr1ngBPrgitLxBI9gBamXvP5wqSXMqHnxAJn0BKvgu
% HDwzZbqegm0B1jxALjhiov2DaeHbuLwBLnhiov2DGi1BTfMBaebbnr
% fifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0xc9
% pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFv
% e9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaakeaacqGH1ecW
% daWgaaWcbaGaaGimaaqabaaaaa!463B!$$
{\aleph }_{0}
$$ parts then there is one
in which F assumes all
values.