CREATE TABLE #Grid
(v1 SMALLINT NOT NULL CHECK (v1 > 0), 
v2 SMALLINT NOT NULL CHECK (v2 > 0), 
PRIMARY KEY (v1, v2), 
CHECK (v1 < v2));

INSERT INTO #Grid (v1, v2)
VALUES (1, 2), (1, 4), (2, 3), (2, 5), (2, 6); 

DECLARE @Covers TABLE 
    (v SMALLINT         -- Covering vertex
    ,vn VARCHAR(8000))  -- Covered vertices

WHILE EXISTS (
    SELECT v
    FROM #Grid
    CROSS APPLY (VALUES (v1),(v2)) a (v)
    EXCEPT
    SELECT Item
    FROM @Covers
    CROSS APPLY DelimitedSplit8K(vn, ',')
)
BEGIN

WHILE EXISTS (
    SELECT v
    FROM #Grid
    CROSS APPLY (VALUES (v1),(v2)) a (v)
    EXCEPT
    SELECT Item
    FROM @Covers
    CROSS APPLY DelimitedSplit8K(vn, ',')
)
BEGIN

    ;WITH Counts AS (
        SELECT v, n=COUNT(v)
        FROM (
            SELECT v
            FROM #Grid
            CROSS APPLY (VALUES (v1),(v2)) a (v)
            WHERE v NOT IN (
                SELECT Item
                FROM @Covers
                CROSS APPLY DelimitedSplit8K(vn, ','))) a  
        GROUP BY v)
    INSERT INTO @Covers 
    --OUTPUT INSERTED.*
    SELECT v, CAST(a.v AS VARCHAR(5)) + (
        SELECT ',' + CASE WHEN v=v2 THEN CAST(v1 AS VARCHAR(5)) ELSE CAST(v2 AS VARCHAR(5)) END
        FROM #Grid b
        WHERE a.v = b.v1 OR a.v = b.v2
        FOR XML PATH(''))
    FROM (
        SELECT TOP 1 v
        FROM Counts
        ORDER BY n DESC, v) a

END

END

SELECT * 
FROM @Covers

DROP TABLE #Grid

USE tempdb
GO
IF OBJECT_ID('tempdb.dbo.Grid') IS NOT NULL DROP TABLE Grid
DECLARE @MinCover TABLE  (Node INT)
DECLARE @Node INT
CREATE TABLE dbo.Grid
(     
     v1			INT
	,v2         INT
    ,Processed	BIT
);

INSERT INTO Grid (v1, v2, Processed)
VALUES (1, 2, 0), (1, 4, 0), (2, 3, 0), (2, 5, 0), (2, 6, 0); 

WHILE EXISTS (SELECT * FROM Grid WHERE Processed = 0)
BEGIN
       ;WITH NodeOcc AS
       (
              SELECT Node   = v1
              FROM Grid
              UNION ALL 
              SELECT v2
              FROM Grid
       )
       INSERT INTO @MinCover
       SELECT TOP 1 Node
       FROM NodeOcc
       WHERE Node NOT IN (SELECT Node FROM @MinCover)
       GROUP BY Node
       ORDER BY COUNT(*) DESC

       UPDATE G
       SET Processed = 1
       FROM Grid                  G
       JOIN @MinCover       NN ON G.v1 = NN.Node OR G.v2 = NN.Node
END

SELECT *
FROM @MinCover