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If G is edge-L-colorable for every edge assignment L with vertical bar L(e)vertical bar >= k for e is an element of E(G), then G is said to be edge-k-choosable.
TL;DR: In this paper, it was shown that a planar graph G with maximum degree Deltageq8 is k-colorable if every 5-cycle of G is not simultaneously adjacent to 3- ...
We prove that if a triangle-free planar graph is not 3-choosable, then it contains a 4-cycle that intersects another 4- or 5-cycle in exactly one edge. This ...
It is known that every planar graph with cycles of length neither 4 nor $k$ for some $k\in\{5,6,7,8,9\}$ is $(3,1)$-choosable. In this paper, we prove that ...
Namely, every planar graph without cycles of length 4, 7 and 9 is 3-colorable. Lastly, we try to get rid of the restriction of lacking 4-cycles to the graphs ...
Missing: chordal | Show results with:chordal
If either Δ ≥ 6 , or Δ = 5 and G contains no 4-cycles with a chord or no 6-cycles with a chord, then G is edge- ( Δ + 1 ) -choosable, where Δ denotes the ...
Missing: chordal | Show results with:chordal
In this paper, we prove that if G is a planar graph with maximum degree Delta(G) not equal 5 and without adjacent 3-cycles, or with maximum degree Delta(G) not ...
Cushing and Kierstead [2] constructively proved that every planar graph is (4, 1)∗-choosable which perfectly solved the last remaining question left open in [3] ...
May 13, 2014 · Liu, J. Cai, Edge-choosability of planar graphs without adjacent triangles or without. 7-cycle, Discrete Mathematics, 309 (2009) 77–84.
In addition, this implies that every triangle-free planar graph without 6- and 7-cycles is 3-choosable. ... cycle of length at most 7 does not have a chord.