Sufficient conditions for a planar graph to be list edgeΔ-colorable and list totally(Δ+1)-colorable
نویسندگان
چکیده
منابع مشابه
A sufficient condition for planar graphs to be 3-colorable
Planar graphs without 3-cycles at distance less than 4 and without 5-cycles are proved to be 3-colorable. We conjecture that, moreover, each plane graph with neither 5-cycles nor intersecting 3-cycles is 3-colorable. In this conjecture, none of the two assumptions can be dropped because there exist planar 4-chromatic graphs without 5-cycles, as well as planar 4chromatic graphs without intersect...
متن کاملOn Uniquely List Colorable Graphs
Let G be a graph with n vertices and suppose that for each vertex v in G, there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k–list colorable graph. Recently M. Mahdian and E.S. Mahmoodian characterized uniquely 2–list colorable graphs. Here we state some results which will pave the way in character...
متن کاملUniquely 2-list colorable graphs
A graph is called to be uniquely list colorable, if it admits a list assignment which induces a unique list coloring. We study uniquely list colorable graphs with a restriction on the number of colors used. In this way we generalize a theorem which characterizes uniquely 2–list colorable graphs. We introduce the uniquely list chromatic number of a graph and make a conjecture about it which is a...
متن کاملThe stipulation polynomial of a uniquely list-colorable graph
Let G be graph and let S be a set of lists of colon; at the vertices G is said to be S list-colorable if there exists a proper' /'rllnr"'Hl of G sllch that each vertexi takes its color . Alan and Tarsi! I] have shown that G is S list-colorable if and only if its graph polynomial fC(;1;..):= IT(Xi Xj) i~J does not lie in the ideal I generated by the annihilator polynomials colors available at th...
متن کاملOn the Uniquely List Colorable Graphs
Let G be a graph with ν vertices, and let S1, S2, . . . , Sν be a list of colors on its vertices, each of size k. If there exists a unique proper coloring for G from this list of colors, then G is called uniquely k–list colorable graph. We characterize all uniquely 2–list colorable graphs, and discuss uniquely k–list colorable graphs by introducing some open problems. We also show the connectio...
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: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.11.026